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- Derivative of:
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Derivative of sin(4x)
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Derivative of x^e
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Derivative of (x^3-1)(x^2+x+1)
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Derivative of log(x+2)
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Identical expressions
- e^sinx*arctg3x*(x)/lnx
- e to the power of sinus of x multiply by arctg3x multiply by (x) divide by lnx
- esinx*arctg3x*(x)/lnx
- esinx*arctg3x*x/lnx
- e^sinxarctg3x(x)/lnx
- esinxarctg3x(x)/lnx
- esinxarctg3xx/lnx
- e^sinxarctg3xx/lnx
- e^sinx*arctg3x*(x) divide by lnx
Derivative of e^sinx*arctg3x*(x)/lnx
The solution
You have entered
[src]
sin(x)
E *atan(3*x)*x
-------------------
log(x)
$$\frac{x e^{\sin{\left(x \right)}} \operatorname{atan}{\left(3 x \right)}}{\log{\left(x \right)}}$$
((E^sin(x)*atan(3*x))*x)/log(x)
The first derivative
[src]
/ sin(x) \
|3*e sin(x)| sin(x)
x*|--------- + atan(3*x)*cos(x)*e | + E *atan(3*x)
| 2 | sin(x)
\ 1 + 9*x / atan(3*x)*e
------------------------------------------------------------ - -----------------
log(x) 2
log (x)
$$\frac{e^{\sin{\left(x \right)}} \operatorname{atan}{\left(3 x \right)} + x \left(e^{\sin{\left(x \right)}} \cos{\left(x \right)} \operatorname{atan}{\left(3 x \right)} + \frac{3 e^{\sin{\left(x \right)}}}{9 x^{2} + 1}\right)}{\log{\left(x \right)}} - \frac{e^{\sin{\left(x \right)}} \operatorname{atan}{\left(3 x \right)}}{\log{\left(x \right)}^{2}}$$
The second derivative
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/ / / 3 \ \ \
| 2*|x*|-------- + atan(3*x)*cos(x)| + atan(3*x)| / 2 \ |
| | | 2 | | |1 + ------|*atan(3*x)|
| 6 // 2 \ 6*cos(x) 54*x \ \ \1 + 9*x / / \ log(x)/ | sin(x)
|-------- - x*|\- cos (x) + sin(x)/*atan(3*x) - -------- + -----------| + 2*atan(3*x)*cos(x) - ----------------------------------------------- + ----------------------|*e
| 2 | 2 2| x*log(x) x*log(x) |
|1 + 9*x | 1 + 9*x / 2\ | |
\ \ \1 + 9*x / / /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
log(x)
$$\frac{\left(- x \left(\frac{54 x}{\left(9 x^{2} + 1\right)^{2}} + \left(\sin{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \operatorname{atan}{\left(3 x \right)} - \frac{6 \cos{\left(x \right)}}{9 x^{2} + 1}\right) + 2 \cos{\left(x \right)} \operatorname{atan}{\left(3 x \right)} + \frac{6}{9 x^{2} + 1} + \frac{\left(1 + \frac{2}{\log{\left(x \right)}}\right) \operatorname{atan}{\left(3 x \right)}}{x \log{\left(x \right)}} - \frac{2 \left(x \left(\cos{\left(x \right)} \operatorname{atan}{\left(3 x \right)} + \frac{3}{9 x^{2} + 1}\right) + \operatorname{atan}{\left(3 x \right)}\right)}{x \log{\left(x \right)}}\right) e^{\sin{\left(x \right)}}}{\log{\left(x \right)}}$$
The third derivative
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/ / / 2 \ \ / 6 // 2 \ 6*cos(x) 54*x \ \ \
| | | 36*x | | 3*|-------- - x*|\- cos (x) + sin(x)/*atan(3*x) - -------- + -----------| + 2*atan(3*x)*cos(x)| / 3 3 \ / 2 \ / / 3 \ \|
| | 54*|-1 + --------| | | 2 | 2 2| | 2*|1 + ------ + -------|*atan(3*x) 3*|1 + ------|*|x*|-------- + atan(3*x)*cos(x)| + atan(3*x)||
| | | 2| / 2 \ | |1 + 9*x | 1 + 9*x / 2\ | | | log(x) 2 | \ log(x)/ | | 2 | ||
| | \ 1 + 9*x / 9*\- cos (x) + sin(x)/ / 2 \ 162*x*cos(x)| 162*x / 2 \ 18*cos(x) \ \ \1 + 9*x / / / \ log (x)/ \ \1 + 9*x / /| sin(x)
|- x*|- ------------------ + ---------------------- + \1 - cos (x) + 3*sin(x)/*atan(3*x)*cos(x) + ------------| - ----------- - 3*\- cos (x) + sin(x)/*atan(3*x) + --------- - ----------------------------------------------------------------------------------------------- - ---------------------------------- + ------------------------------------------------------------|*e
| | 2 2 2 | 2 2 x*log(x) 2 2 |
| | / 2\ 1 + 9*x / 2\ | / 2\ 1 + 9*x x *log(x) x *log(x) |
\ \ \1 + 9*x / \1 + 9*x / / \1 + 9*x / /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
log(x)
$$\frac{\left(- x \left(\frac{162 x \cos{\left(x \right)}}{\left(9 x^{2} + 1\right)^{2}} + \left(3 \sin{\left(x \right)} - \cos^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)} \operatorname{atan}{\left(3 x \right)} + \frac{9 \left(\sin{\left(x \right)} - \cos^{2}{\left(x \right)}\right)}{9 x^{2} + 1} - \frac{54 \left(\frac{36 x^{2}}{9 x^{2} + 1} - 1\right)}{\left(9 x^{2} + 1\right)^{2}}\right) - \frac{162 x}{\left(9 x^{2} + 1\right)^{2}} - 3 \left(\sin{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \operatorname{atan}{\left(3 x \right)} + \frac{18 \cos{\left(x \right)}}{9 x^{2} + 1} - \frac{3 \left(- x \left(\frac{54 x}{\left(9 x^{2} + 1\right)^{2}} + \left(\sin{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \operatorname{atan}{\left(3 x \right)} - \frac{6 \cos{\left(x \right)}}{9 x^{2} + 1}\right) + 2 \cos{\left(x \right)} \operatorname{atan}{\left(3 x \right)} + \frac{6}{9 x^{2} + 1}\right)}{x \log{\left(x \right)}} + \frac{3 \left(1 + \frac{2}{\log{\left(x \right)}}\right) \left(x \left(\cos{\left(x \right)} \operatorname{atan}{\left(3 x \right)} + \frac{3}{9 x^{2} + 1}\right) + \operatorname{atan}{\left(3 x \right)}\right)}{x^{2} \log{\left(x \right)}} - \frac{2 \left(1 + \frac{3}{\log{\left(x \right)}} + \frac{3}{\log{\left(x \right)}^{2}}\right) \operatorname{atan}{\left(3 x \right)}}{x^{2} \log{\left(x \right)}}\right) e^{\sin{\left(x \right)}}}{\log{\left(x \right)}}$$