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How to use it?
- Derivative of:
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Derivative of log(x^2+5)
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Derivative of e^(-2*x)
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Derivative of sin(x)-x*cos(x)
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Derivative of e^x*x
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Identical expressions
- five ^arctg^ two (ln(x+ one)/(sin2x))
- 5 to the power of arctg squared (ln(x plus 1) divide by ( sinus of 2x))
- five to the power of arctg to the power of two (ln(x plus one) divide by ( sinus of 2x))
- 5arctg2(ln(x+1)/(sin2x))
- 5arctg2lnx+1/sin2x
- 5^arctg²(ln(x+1)/(sin2x))
- 5 to the power of arctg to the power of 2(ln(x+1)/(sin2x))
- 5^arctg^2lnx+1/sin2x
- 5^arctg^2(ln(x+1) divide by (sin2x))
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Similar expressions
- 5^arctg^2(ln(x-1)/(sin2x))
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What you mean?
- 5^(atan(log(x + 1)/sin(2*x))^2)
- 5^(atan(log(x + 1)/((sin(2)*x)))^2)
- 5^(atan(log(x + 1)*2*x/sin(x))^2)
- 5^(atan(log(x + 1)/sin(2*x))^2)
- 5^(atan(log(x + 1)/((sin(2)*x)))^2)
- 5^(atan(log(x + 1)*2*x/sin(x))^2)
- 5^(atan(log(x + 1)*2*x/sin(x))^2)
You entered:
5^arctg^2(ln(x+1)/(sin2x))
What you mean?
Derivative of 5^arctg^2(ln(x+1)/(sin2x))
The solution
You have entered
[src]
2/log(x + 1)\
atan |----------|
\ sin(2*x) /
5
$$5^{\operatorname{atan}^{2}{\left(\frac{\log{\left(x + 1 \right)}}{\sin{\left(2 x \right)}} \right)}}$$
/ 2/log(x + 1)\\ | atan |----------|| d | \ sin(2*x) /| --\5 / dx
$$\frac{d}{d x} 5^{\operatorname{atan}^{2}{\left(\frac{\log{\left(x + 1 \right)}}{\sin{\left(2 x \right)}} \right)}}$$
The first derivative
[src]
2/log(x + 1)\
atan |----------|
\ sin(2*x) / / 1 2*cos(2*x)*log(x + 1)\ /log(x + 1)\
2*5 *|---------------- - ---------------------|*atan|----------|*log(5)
|(x + 1)*sin(2*x) 2 | \ sin(2*x) /
\ sin (2*x) /
---------------------------------------------------------------------------------------
2
log (x + 1)
1 + -----------
2
sin (2*x)
$$\frac{2 \cdot 5^{\operatorname{atan}^{2}{\left(\frac{\log{\left(x + 1 \right)}}{\sin{\left(2 x \right)}} \right)}} \left(- \frac{2 \log{\left(x + 1 \right)} \cos{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}} + \frac{1}{\left(x + 1\right) \sin{\left(2 x \right)}}\right) \log{\left(5 \right)} \operatorname{atan}{\left(\frac{\log{\left(x + 1 \right)}}{\sin{\left(2 x \right)}} \right)}}{\frac{\log{\left(x + 1 \right)}^{2}}{\sin^{2}{\left(2 x \right)}} + 1}$$
The second derivative
[src]
/ 2 2 2 \
2/log(1 + x)\ | / 1 2*cos(2*x)*log(1 + x)\ / 1 2*cos(2*x)*log(1 + x)\ /log(1 + x)\ / 1 2*cos(2*x)*log(1 + x)\ 2/log(1 + x)\ |
atan |----------| |/ 2 \ |- ----- + ---------------------| 2*|- ----- + ---------------------| *atan|----------|*log(1 + x) 2*|- ----- + ---------------------| *atan |----------|*log(5)|
\ sin(2*x) / || 1 4*cos(2*x) 8*cos (2*x)*log(1 + x)| /log(1 + x)\ \ 1 + x sin(2*x) / \ 1 + x sin(2*x) / \ sin(2*x) / \ 1 + x sin(2*x) / \ sin(2*x) / |
2*5 *||- -------- + 4*log(1 + x) - ---------------- + ----------------------|*atan|----------| + ---------------------------------- - ---------------------------------------------------------------- + -------------------------------------------------------------|*log(5)
|| 2 (1 + x)*sin(2*x) 2 | \ sin(2*x) / / 2 \ / 2 \ / 2 \ |
|\ (1 + x) sin (2*x) / | log (1 + x)| | log (1 + x)| 2 | log (1 + x)| |
| |1 + -----------|*sin(2*x) |1 + -----------|*sin (2*x) |1 + -----------|*sin(2*x) |
| | 2 | | 2 | | 2 | |
\ \ sin (2*x) / \ sin (2*x) / \ sin (2*x) / /
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/ 2 \
| log (1 + x)|
|1 + -----------|*sin(2*x)
| 2 |
\ sin (2*x) /
$$\frac{2 \cdot 5^{\operatorname{atan}^{2}{\left(\frac{\log{\left(x + 1 \right)}}{\sin{\left(2 x \right)}} \right)}} \left(\left(4 \log{\left(x + 1 \right)} + \frac{8 \log{\left(x + 1 \right)} \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}} - \frac{4 \cos{\left(2 x \right)}}{\left(x + 1\right) \sin{\left(2 x \right)}} - \frac{1}{\left(x + 1\right)^{2}}\right) \operatorname{atan}{\left(\frac{\log{\left(x + 1 \right)}}{\sin{\left(2 x \right)}} \right)} - \frac{2 \left(\frac{2 \log{\left(x + 1 \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} - \frac{1}{x + 1}\right)^{2} \log{\left(x + 1 \right)} \operatorname{atan}{\left(\frac{\log{\left(x + 1 \right)}}{\sin{\left(2 x \right)}} \right)}}{\left(\frac{\log{\left(x + 1 \right)}^{2}}{\sin^{2}{\left(2 x \right)}} + 1\right) \sin^{2}{\left(2 x \right)}} + \frac{2 \left(\frac{2 \log{\left(x + 1 \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} - \frac{1}{x + 1}\right)^{2} \log{\left(5 \right)} \operatorname{atan}^{2}{\left(\frac{\log{\left(x + 1 \right)}}{\sin{\left(2 x \right)}} \right)}}{\left(\frac{\log{\left(x + 1 \right)}^{2}}{\sin^{2}{\left(2 x \right)}} + 1\right) \sin{\left(2 x \right)}} + \frac{\left(\frac{2 \log{\left(x + 1 \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} - \frac{1}{x + 1}\right)^{2}}{\left(\frac{\log{\left(x + 1 \right)}^{2}}{\sin^{2}{\left(2 x \right)}} + 1\right) \sin{\left(2 x \right)}}\right) \log{\left(5 \right)}}{\left(\frac{\log{\left(x + 1 \right)}^{2}}{\sin^{2}{\left(2 x \right)}} + 1\right) \sin{\left(2 x \right)}}$$
The third derivative
[src]
/ / 2 \ / 2 2 \ / 2 \ / 2 \ \
| / 1 2*cos(2*x)*log(1 + x)\ | 1 4*cos(2*x) 8*cos (2*x)*log(1 + x)| 3 3 3 3 / 1 2*cos(2*x)*log(1 + x)\ | 1 2 log(1 + x) 12*cos (2*x)*log (1 + x) 8*cos(2*x)*log(1 + x)| /log(1 + x)\ 2/log(1 + x)\ / 1 2*cos(2*x)*log(1 + x)\ | 1 4*cos(2*x) 8*cos (2*x)*log(1 + x)| / 1 2*cos(2*x)*log(1 + x)\ | 1 4*cos(2*x) 8*cos (2*x)*log(1 + x)| /log(1 + x)\ 3 |
2/log(1 + x)\ | 3*|- ----- + ---------------------|*|- -------- + 4*log(1 + x) - ---------------- + ----------------------| / 1 2*cos(2*x)*log(1 + x)\ / 1 2*cos(2*x)*log(1 + x)\ 2 /log(1 + x)\ / 1 2*cos(2*x)*log(1 + x)\ /log(1 + x)\ / 1 2*cos(2*x)*log(1 + x)\ 3/log(1 + x)\ 2 2*|- ----- + ---------------------|*|-------- + 4*log (1 + x) - ---------- + ------------------------ - ---------------------|*atan|----------| 6*atan |----------|*|- ----- + ---------------------|*|- -------- + 4*log(1 + x) - ---------------- + ----------------------|*log(5) 4*|- ----- + ---------------------|*|- -------- + 4*log(1 + x) - ---------------- + ----------------------|*atan|----------|*log(1 + x) / 1 2*cos(2*x)*log(1 + x)\ 2/log(1 + x)\ |
atan |----------| | / 3 2 \ \ 1 + x sin(2*x) / | 2 (1 + x)*sin(2*x) 2 | 6*|- ----- + ---------------------| *log(1 + x) 8*|- ----- + ---------------------| *log (1 + x)*atan|----------| 6*|- ----- + ---------------------| *atan|----------|*log(5) 4*|- ----- + ---------------------| *atan |----------|*log (5) \ 1 + x sin(2*x) / | 2 2 2 (1 + x)*sin(2*x) | \ sin(2*x) / \ sin(2*x) / \ 1 + x sin(2*x) / | 2 (1 + x)*sin(2*x) 2 | \ 1 + x sin(2*x) / | 2 (1 + x)*sin(2*x) 2 | \ sin(2*x) / 12*|- ----- + ---------------------| *atan |----------|*log(5)*log(1 + x)|
\ sin(2*x) / | | 1 6 24*cos (2*x)*log(1 + x) 20*cos(2*x)*log(1 + x) 3*cos(2*x) 12*cos (2*x) | /log(1 + x)\ \ (1 + x) sin (2*x) / \ 1 + x sin(2*x) / \ 1 + x sin(2*x) / \ sin(2*x) / \ 1 + x sin(2*x) / \ sin(2*x) / \ 1 + x sin(2*x) / \ sin(2*x) / \(1 + x) (1 + x) sin (2*x) / \ (1 + x) sin (2*x) / \ (1 + x) sin (2*x) / \ 1 + x sin(2*x) / \ sin(2*x) / |
2*5 *|2*|-------- + ----- - ----------------------- - ---------------------- + ----------------- + -----------------|*atan|----------| - ----------------------------------------------------------------------------------------------------------- + ----------------------------------------------- - ----------------------------------------------------------------- - ------------------------------------------------------------ - -------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------|*log(5)
| | 3 1 + x 3 sin(2*x) 2 2 | \ sin(2*x) / / 2 \ 2 2 2 2 / 2 \ / 2 \ / 2 \ 2 |
| \(1 + x) sin (2*x) (1 + x) *sin(2*x) (1 + x)*sin (2*x)/ | log (1 + x)| / 2 \ / 2 \ / 2 \ / 2 \ | log (1 + x)| 2 | log (1 + x)| | log (1 + x)| 2 / 2 \ |
| |1 + -----------|*sin(2*x) | log (1 + x)| 3 | log (1 + x)| 4 | log (1 + x)| 2 | log (1 + x)| 2 |1 + -----------|*sin (2*x) |1 + -----------|*sin(2*x) |1 + -----------|*sin (2*x) | log (1 + x)| 3 |
| | 2 | |1 + -----------| *sin (2*x) |1 + -----------| *sin (2*x) |1 + -----------| *sin (2*x) |1 + -----------| *sin (2*x) | 2 | | 2 | | 2 | |1 + -----------| *sin (2*x) |
| \ sin (2*x) / | 2 | | 2 | | 2 | | 2 | \ sin (2*x) / \ sin (2*x) / \ sin (2*x) / | 2 | |
\ \ sin (2*x) / \ sin (2*x) / \ sin (2*x) / \ sin (2*x) / \ sin (2*x) / /
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/ 2 \
| log (1 + x)|
|1 + -----------|*sin(2*x)
| 2 |
\ sin (2*x) /
$$\frac{2 \cdot 5^{\operatorname{atan}^{2}{\left(\frac{\log{\left(x + 1 \right)}}{\sin{\left(2 x \right)}} \right)}} \left(2 \left(- \frac{20 \log{\left(x + 1 \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} - \frac{24 \log{\left(x + 1 \right)} \cos^{3}{\left(2 x \right)}}{\sin^{3}{\left(2 x \right)}} + \frac{6}{x + 1} + \frac{12 \cos^{2}{\left(2 x \right)}}{\left(x + 1\right) \sin^{2}{\left(2 x \right)}} + \frac{3 \cos{\left(2 x \right)}}{\left(x + 1\right)^{2} \sin{\left(2 x \right)}} + \frac{1}{\left(x + 1\right)^{3}}\right) \operatorname{atan}{\left(\frac{\log{\left(x + 1 \right)}}{\sin{\left(2 x \right)}} \right)} + \frac{4 \cdot \left(\frac{2 \log{\left(x + 1 \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} - \frac{1}{x + 1}\right) \left(4 \log{\left(x + 1 \right)} + \frac{8 \log{\left(x + 1 \right)} \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}} - \frac{4 \cos{\left(2 x \right)}}{\left(x + 1\right) \sin{\left(2 x \right)}} - \frac{1}{\left(x + 1\right)^{2}}\right) \log{\left(x + 1 \right)} \operatorname{atan}{\left(\frac{\log{\left(x + 1 \right)}}{\sin{\left(2 x \right)}} \right)}}{\left(\frac{\log{\left(x + 1 \right)}^{2}}{\sin^{2}{\left(2 x \right)}} + 1\right) \sin^{2}{\left(2 x \right)}} - \frac{6 \cdot \left(\frac{2 \log{\left(x + 1 \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} - \frac{1}{x + 1}\right) \left(4 \log{\left(x + 1 \right)} + \frac{8 \log{\left(x + 1 \right)} \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}} - \frac{4 \cos{\left(2 x \right)}}{\left(x + 1\right) \sin{\left(2 x \right)}} - \frac{1}{\left(x + 1\right)^{2}}\right) \log{\left(5 \right)} \operatorname{atan}^{2}{\left(\frac{\log{\left(x + 1 \right)}}{\sin{\left(2 x \right)}} \right)}}{\left(\frac{\log{\left(x + 1 \right)}^{2}}{\sin^{2}{\left(2 x \right)}} + 1\right) \sin{\left(2 x \right)}} - \frac{3 \cdot \left(\frac{2 \log{\left(x + 1 \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} - \frac{1}{x + 1}\right) \left(4 \log{\left(x + 1 \right)} + \frac{8 \log{\left(x + 1 \right)} \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}} - \frac{4 \cos{\left(2 x \right)}}{\left(x + 1\right) \sin{\left(2 x \right)}} - \frac{1}{\left(x + 1\right)^{2}}\right)}{\left(\frac{\log{\left(x + 1 \right)}^{2}}{\sin^{2}{\left(2 x \right)}} + 1\right) \sin{\left(2 x \right)}} + \frac{2 \cdot \left(\frac{2 \log{\left(x + 1 \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} - \frac{1}{x + 1}\right) \left(4 \log{\left(x + 1 \right)}^{2} + \frac{12 \log{\left(x + 1 \right)}^{2} \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}} - \frac{8 \log{\left(x + 1 \right)} \cos{\left(2 x \right)}}{\left(x + 1\right) \sin{\left(2 x \right)}} - \frac{\log{\left(x + 1 \right)}}{\left(x + 1\right)^{2}} + \frac{1}{\left(x + 1\right)^{2}}\right) \operatorname{atan}{\left(\frac{\log{\left(x + 1 \right)}}{\sin{\left(2 x \right)}} \right)}}{\left(\frac{\log{\left(x + 1 \right)}^{2}}{\sin^{2}{\left(2 x \right)}} + 1\right) \sin^{2}{\left(2 x \right)}} - \frac{8 \left(\frac{2 \log{\left(x + 1 \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} - \frac{1}{x + 1}\right)^{3} \log{\left(x + 1 \right)}^{2} \operatorname{atan}{\left(\frac{\log{\left(x + 1 \right)}}{\sin{\left(2 x \right)}} \right)}}{\left(\frac{\log{\left(x + 1 \right)}^{2}}{\sin^{2}{\left(2 x \right)}} + 1\right)^{2} \sin^{4}{\left(2 x \right)}} + \frac{12 \left(\frac{2 \log{\left(x + 1 \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} - \frac{1}{x + 1}\right)^{3} \log{\left(5 \right)} \log{\left(x + 1 \right)} \operatorname{atan}^{2}{\left(\frac{\log{\left(x + 1 \right)}}{\sin{\left(2 x \right)}} \right)}}{\left(\frac{\log{\left(x + 1 \right)}^{2}}{\sin^{2}{\left(2 x \right)}} + 1\right)^{2} \sin^{3}{\left(2 x \right)}} + \frac{6 \left(\frac{2 \log{\left(x + 1 \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} - \frac{1}{x + 1}\right)^{3} \log{\left(x + 1 \right)}}{\left(\frac{\log{\left(x + 1 \right)}^{2}}{\sin^{2}{\left(2 x \right)}} + 1\right)^{2} \sin^{3}{\left(2 x \right)}} - \frac{4 \left(\frac{2 \log{\left(x + 1 \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} - \frac{1}{x + 1}\right)^{3} \log{\left(5 \right)}^{2} \operatorname{atan}^{3}{\left(\frac{\log{\left(x + 1 \right)}}{\sin{\left(2 x \right)}} \right)}}{\left(\frac{\log{\left(x + 1 \right)}^{2}}{\sin^{2}{\left(2 x \right)}} + 1\right)^{2} \sin^{2}{\left(2 x \right)}} - \frac{6 \left(\frac{2 \log{\left(x + 1 \right)} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} - \frac{1}{x + 1}\right)^{3} \log{\left(5 \right)} \operatorname{atan}{\left(\frac{\log{\left(x + 1 \right)}}{\sin{\left(2 x \right)}} \right)}}{\left(\frac{\log{\left(x + 1 \right)}^{2}}{\sin^{2}{\left(2 x \right)}} + 1\right)^{2} \sin^{2}{\left(2 x \right)}}\right) \log{\left(5 \right)}}{\left(\frac{\log{\left(x + 1 \right)}^{2}}{\sin^{2}{\left(2 x \right)}} + 1\right) \sin{\left(2 x \right)}}$$
The graph