Mister Exam
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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Derivative of:
- Derivative of e^x^x
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Derivative of x/(x-4)
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Derivative of tan(e^(2*x))
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Derivative of sin^3*x
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Identical expressions
- (ctg3x)^cos4x
- (ctg3x) to the power of co sinus of e of 4x
- (ctg3x)cos4x
- ctg3xcos4x
- ctg3x^cos4x
Derivative of (ctg3x)^cos4x
The solution
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[src]
cos(4*x) cot (3*x)
$$\cot^{\cos{\left(4 x \right)}}{\left(3 x \right)}$$
cot(3*x)^cos(4*x)
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
The answer is:
The first derivative
[src]
/ / 2 \ \
cos(4*x) | \-3 - 3*cot (3*x)/*cos(4*x)|
cot (3*x)*|-4*log(cot(3*x))*sin(4*x) + ---------------------------|
\ cot(3*x) /
$$\left(\frac{\left(- 3 \cot^{2}{\left(3 x \right)} - 3\right) \cos{\left(4 x \right)}}{\cot{\left(3 x \right)}} - 4 \log{\left(\cot{\left(3 x \right)} \right)} \sin{\left(4 x \right)}\right) \cot^{\cos{\left(4 x \right)}}{\left(3 x \right)}$$
The second derivative
[src]
/ 2 2 \
|/ / 2 \ \ / 2 \ / 2 \ |
cos(4*x) || 3*\1 + cot (3*x)/*cos(4*x)| / 2 \ 9*\1 + cot (3*x)/ *cos(4*x) 24*\1 + cot (3*x)/*sin(4*x)|
cot (3*x)*||4*log(cot(3*x))*sin(4*x) + --------------------------| - 16*cos(4*x)*log(cot(3*x)) + 18*\1 + cot (3*x)/*cos(4*x) - --------------------------- + ---------------------------|
|\ cot(3*x) / 2 cot(3*x) |
\ cot (3*x) /
$$\left(\left(\frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right) \cos{\left(4 x \right)}}{\cot{\left(3 x \right)}} + 4 \log{\left(\cot{\left(3 x \right)} \right)} \sin{\left(4 x \right)}\right)^{2} - \frac{9 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2} \cos{\left(4 x \right)}}{\cot^{2}{\left(3 x \right)}} + \frac{24 \left(\cot^{2}{\left(3 x \right)} + 1\right) \sin{\left(4 x \right)}}{\cot{\left(3 x \right)}} + 18 \left(\cot^{2}{\left(3 x \right)} + 1\right) \cos{\left(4 x \right)} - 16 \log{\left(\cot{\left(3 x \right)} \right)} \cos{\left(4 x \right)}\right) \cot^{\cos{\left(4 x \right)}}{\left(3 x \right)}$$
The third derivative
[src]
/ 3 / 2 \ 3 2 2 \
| / / 2 \ \ / / 2 \ \ | / 2 \ / 2 \ | / 2 \ / 2 \ / 2 \ / 2 \ |
cos(4*x) | | 3*\1 + cot (3*x)/*cos(4*x)| / 2 \ | 3*\1 + cot (3*x)/*cos(4*x)| | / 2 \ 24*\1 + cot (3*x)/*sin(4*x) 9*\1 + cot (3*x)/ *cos(4*x)| / 2 \ 54*\1 + cot (3*x)/ *cos(4*x) 108*\1 + cot (3*x)/ *cos(4*x) 108*\1 + cot (3*x)/ *sin(4*x) 144*\1 + cot (3*x)/*cos(4*x)|
cot (3*x)*|- |4*log(cot(3*x))*sin(4*x) + --------------------------| - 216*\1 + cot (3*x)/*sin(4*x) + 3*|4*log(cot(3*x))*sin(4*x) + --------------------------|*|- 18*\1 + cot (3*x)/*cos(4*x) + 16*cos(4*x)*log(cot(3*x)) - --------------------------- + ---------------------------| + 64*log(cot(3*x))*sin(4*x) - 108*\1 + cot (3*x)/*cos(4*x)*cot(3*x) - ---------------------------- + ----------------------------- + ----------------------------- + ----------------------------|
| \ cot(3*x) / \ cot(3*x) / | cot(3*x) 2 | 3 cot(3*x) 2 cot(3*x) |
\ \ cot (3*x) / cot (3*x) cot (3*x) /
$$\left(- \left(\frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right) \cos{\left(4 x \right)}}{\cot{\left(3 x \right)}} + 4 \log{\left(\cot{\left(3 x \right)} \right)} \sin{\left(4 x \right)}\right)^{3} + 3 \left(\frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right) \cos{\left(4 x \right)}}{\cot{\left(3 x \right)}} + 4 \log{\left(\cot{\left(3 x \right)} \right)} \sin{\left(4 x \right)}\right) \left(\frac{9 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2} \cos{\left(4 x \right)}}{\cot^{2}{\left(3 x \right)}} - \frac{24 \left(\cot^{2}{\left(3 x \right)} + 1\right) \sin{\left(4 x \right)}}{\cot{\left(3 x \right)}} - 18 \left(\cot^{2}{\left(3 x \right)} + 1\right) \cos{\left(4 x \right)} + 16 \log{\left(\cot{\left(3 x \right)} \right)} \cos{\left(4 x \right)}\right) - \frac{54 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{3} \cos{\left(4 x \right)}}{\cot^{3}{\left(3 x \right)}} + \frac{108 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2} \sin{\left(4 x \right)}}{\cot^{2}{\left(3 x \right)}} + \frac{108 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2} \cos{\left(4 x \right)}}{\cot{\left(3 x \right)}} - 216 \left(\cot^{2}{\left(3 x \right)} + 1\right) \sin{\left(4 x \right)} - 108 \left(\cot^{2}{\left(3 x \right)} + 1\right) \cos{\left(4 x \right)} \cot{\left(3 x \right)} + \frac{144 \left(\cot^{2}{\left(3 x \right)} + 1\right) \cos{\left(4 x \right)}}{\cot{\left(3 x \right)}} + 64 \log{\left(\cot{\left(3 x \right)} \right)} \sin{\left(4 x \right)}\right) \cot^{\cos{\left(4 x \right)}}{\left(3 x \right)}$$