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- Derivative of:
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Derivative of z
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Derivative of x^2*atanh(x)*acoth(x)
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Derivative of -cos(x)
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Derivative of coth(x)/tanh(x)
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Identical expressions
- (arctan(x))^ three *log2(sin(x))
- (arc tangent of (x)) cubed multiply by logarithm of 2( sinus of (x))
- (arc tangent of (x)) to the power of three multiply by logarithm of 2( sinus of (x))
- (arctan(x))3*log2(sin(x))
- arctanx3*log2sinx
- (arctan(x))³*log2(sin(x))
- (arctan(x)) to the power of 3*log2(sin(x))
- (arctan(x))^3log2(sin(x))
- (arctan(x))3log2(sin(x))
- arctanx3log2sinx
- arctanx^3log2sinx
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Similar expressions
- (arctan(x))^3*log2(sinx)
Derivative of (arctan(x))^3*log2(sin(x))
The solution
You have entered
[src]
3 log(sin(x))
atan (x)*-----------
log(2)
$$\frac{\log{\left(\sin{\left(x \right)} \right)}}{\log{\left(2 \right)}} \operatorname{atan}^{3}{\left(x \right)}$$
atan(x)^3*(log(sin(x))/log(2))
The first derivative
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3 2
atan (x)*cos(x) 3*atan (x)*log(sin(x))
--------------- + ----------------------
log(2)*sin(x) / 2\
\1 + x /*log(2)
$$\frac{\cos{\left(x \right)} \operatorname{atan}^{3}{\left(x \right)}}{\log{\left(2 \right)} \sin{\left(x \right)}} + \frac{3 \log{\left(\sin{\left(x \right)} \right)} \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right) \log{\left(2 \right)}}$$
The second derivative
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/ / 2 \ \
| 2 | cos (x)| 6*(-1 + x*atan(x))*log(sin(x)) 6*atan(x)*cos(x)|
|- atan (x)*|1 + -------| - ------------------------------ + ----------------|*atan(x)
| | 2 | 2 / 2\ |
| \ sin (x)/ / 2\ \1 + x /*sin(x) |
\ \1 + x / /
--------------------------------------------------------------------------------------
log(2)
$$\frac{\left(- \left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \operatorname{atan}^{2}{\left(x \right)} + \frac{6 \cos{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right) \sin{\left(x \right)}} - \frac{6 \left(x \operatorname{atan}{\left(x \right)} - 1\right) \log{\left(\sin{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{2}}\right) \operatorname{atan}{\left(x \right)}}{\log{\left(2 \right)}}$$
The third derivative
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/ 2 \ / 2 2 \ / 2 \
2 | cos (x)| | 1 2 6*x*atan(x) 4*x *atan (x)| 3 | cos (x)|
9*atan (x)*|1 + -------| 6*|------ - atan (x) - ----------- + -------------|*log(sin(x)) 2*atan (x)*|1 + -------|*cos(x)
| 2 | | 2 2 2 | | 2 |
\ sin (x)/ \1 + x 1 + x 1 + x / \ sin (x)/ 18*(-1 + x*atan(x))*atan(x)*cos(x)
- ------------------------ + --------------------------------------------------------------- + ------------------------------- - ----------------------------------
2 2 sin(x) 2
1 + x / 2\ / 2\
\1 + x / \1 + x / *sin(x)
-------------------------------------------------------------------------------------------------------------------------------------------------------------------
log(2)
$$\frac{\frac{2 \left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)} \operatorname{atan}^{3}{\left(x \right)}}{\sin{\left(x \right)}} - \frac{9 \left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{18 \left(x \operatorname{atan}{\left(x \right)} - 1\right) \cos{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \sin{\left(x \right)}} + \frac{6 \left(\frac{4 x^{2} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{6 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \operatorname{atan}^{2}{\left(x \right)} + \frac{1}{x^{2} + 1}\right) \log{\left(\sin{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{2}}}{\log{\left(2 \right)}}$$