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- Derivative of:
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Derivative of y=2x-1
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Derivative of x-ln(1+x)
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Derivative of x*(1-x)
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Derivative of f(x)=1/4x^4+x
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Identical expressions
- arctg(x/ three)*ln(2x+ three)^ three
- arctg(x divide by 3) multiply by ln(2x plus 3) cubed
- arctg(x divide by three) multiply by ln(2x plus three) to the power of three
- arctg(x/3)*ln(2x+3)3
- arctgx/3*ln2x+33
- arctg(x/3)*ln(2x+3)³
- arctg(x/3)*ln(2x+3) to the power of 3
- arctg(x/3)ln(2x+3)^3
- arctg(x/3)ln(2x+3)3
- arctgx/3ln2x+33
- arctgx/3ln2x+3^3
- arctg(x divide by 3)*ln(2x+3)^3
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Similar expressions
- arctg(x/3)*ln(2x-3)^3
Derivative of arctg(x/3)*ln(2x+3)^3
The solution
You have entered
[src]
/x\ 3
atan|-|*log (2*x + 3)
\3/
$$\log{\left(2 x + 3 \right)}^{3} \operatorname{atan}{\left(\frac{x}{3} \right)}$$
atan(x/3)*log(2*x + 3)^3
The first derivative
[src]
2 /x\
3 6*log (2*x + 3)*atan|-|
log (2*x + 3) \3/
------------- + -----------------------
/ 2\ 2*x + 3
| x |
3*|1 + --|
\ 9 /
$$\frac{\log{\left(2 x + 3 \right)}^{3}}{3 \left(\frac{x^{2}}{9} + 1\right)} + \frac{6 \log{\left(2 x + 3 \right)}^{2} \operatorname{atan}{\left(\frac{x}{3} \right)}}{2 x + 3}$$
The second derivative
[src]
/ /x\ \ | 2 2*(-2 + log(3 + 2*x))*atan|-| | | x*log (3 + 2*x) \3/ 6*log(3 + 2*x) | 6*|- --------------- - ----------------------------- + ------------------|*log(3 + 2*x) | 2 2 / 2\| | / 2\ (3 + 2*x) (3 + 2*x)*\9 + x /| \ \9 + x / /
$$6 \left(- \frac{x \log{\left(2 x + 3 \right)}^{2}}{\left(x^{2} + 9\right)^{2}} + \frac{6 \log{\left(2 x + 3 \right)}}{\left(2 x + 3\right) \left(x^{2} + 9\right)} - \frac{2 \left(\log{\left(2 x + 3 \right)} - 2\right) \operatorname{atan}{\left(\frac{x}{3} \right)}}{\left(2 x + 3\right)^{2}}\right) \log{\left(2 x + 3 \right)}$$
The third derivative
[src]
/ / 2 \ \ | 3 | 4*x | | |log (3 + 2*x)*|-1 + ------| / 2 \ /x\ | | | 2| 8*\1 + log (3 + 2*x) - 3*log(3 + 2*x)/*atan|-| 2 | | \ 9 + x / \3/ 18*x*log (3 + 2*x) 18*(-2 + log(3 + 2*x))*log(3 + 2*x)| 6*|--------------------------- + ---------------------------------------------- - ------------------- - -----------------------------------| | 2 3 2 2 / 2\ | | / 2\ (3 + 2*x) / 2\ (3 + 2*x) *\9 + x / | \ \9 + x / (3 + 2*x)*\9 + x / /
$$6 \left(- \frac{18 x \log{\left(2 x + 3 \right)}^{2}}{\left(2 x + 3\right) \left(x^{2} + 9\right)^{2}} + \frac{\left(\frac{4 x^{2}}{x^{2} + 9} - 1\right) \log{\left(2 x + 3 \right)}^{3}}{\left(x^{2} + 9\right)^{2}} - \frac{18 \left(\log{\left(2 x + 3 \right)} - 2\right) \log{\left(2 x + 3 \right)}}{\left(2 x + 3\right)^{2} \left(x^{2} + 9\right)} + \frac{8 \left(\log{\left(2 x + 3 \right)}^{2} - 3 \log{\left(2 x + 3 \right)} + 1\right) \operatorname{atan}{\left(\frac{x}{3} \right)}}{\left(2 x + 3\right)^{3}}\right)$$