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:
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Derivative of x^-6
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Derivative of x^2*sqrt(1-x^2)
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Derivative of x^3*cot(x)
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Derivative of sin(x)+3
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Identical expressions
- (ctg(x))^sin(2x)
- (ctg(x)) to the power of sinus of (2x)
- (ctg(x))sin(2x)
- ctgxsin2x
- ctgx^sin2x
Derivative of (ctg(x))^sin(2x)
The solution
You have entered
[src]
sin(2*x) cot (x)
$$\cot^{\sin{\left(2 x \right)}}{\left(x \right)}$$
cot(x)^sin(2*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
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/ / 2 \ \
sin(2*x) | \-1 - cot (x)/*sin(2*x)|
cot (x)*|2*cos(2*x)*log(cot(x)) + -----------------------|
\ cot(x) /
$$\left(\frac{\left(- \cot^{2}{\left(x \right)} - 1\right) \sin{\left(2 x \right)}}{\cot{\left(x \right)}} + 2 \log{\left(\cot{\left(x \right)} \right)} \cos{\left(2 x \right)}\right) \cot^{\sin{\left(2 x \right)}}{\left(x \right)}$$
The second derivative
[src]
/ 2 2 \
|/ / 2 \ \ / 2 \ / 2 \ |
sin(2*x) || \1 + cot (x)/*sin(2*x)| / 2 \ \1 + cot (x)/ *sin(2*x) 4*\1 + cot (x)/*cos(2*x)|
cot (x)*||-2*cos(2*x)*log(cot(x)) + ----------------------| - 4*log(cot(x))*sin(2*x) + 2*\1 + cot (x)/*sin(2*x) - ----------------------- - ------------------------|
|\ cot(x) / 2 cot(x) |
\ cot (x) /
$$\left(\left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)}}{\cot{\left(x \right)}} - 2 \log{\left(\cot{\left(x \right)} \right)} \cos{\left(2 x \right)}\right)^{2} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(2 x \right)}}{\cot^{2}{\left(x \right)}} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)} - \frac{4 \left(\cot^{2}{\left(x \right)} + 1\right) \cos{\left(2 x \right)}}{\cot{\left(x \right)}} - 4 \log{\left(\cot{\left(x \right)} \right)} \sin{\left(2 x \right)}\right) \cot^{\sin{\left(2 x \right)}}{\left(x \right)}$$
The third derivative
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/ 3 / 2 \ 2 3 2 \
| / / 2 \ \ / / 2 \ \ | / 2 \ / 2 \ | / 2 \ / 2 \ / 2 \ / 2 \ |
sin(2*x) | | \1 + cot (x)/*sin(2*x)| | \1 + cot (x)/*sin(2*x)| | / 2 \ \1 + cot (x)/ *sin(2*x) 4*\1 + cot (x)/*cos(2*x)| / 2 \ 6*\1 + cot (x)/ *cos(2*x) / 2 \ 2*\1 + cot (x)/ *sin(2*x) 4*\1 + cot (x)/ *sin(2*x) 12*\1 + cot (x)/*sin(2*x)|
cot (x)*|- |-2*cos(2*x)*log(cot(x)) + ----------------------| - 8*cos(2*x)*log(cot(x)) + 3*|-2*cos(2*x)*log(cot(x)) + ----------------------|*|- 2*\1 + cot (x)/*sin(2*x) + 4*log(cot(x))*sin(2*x) + ----------------------- + ------------------------| + 12*\1 + cot (x)/*cos(2*x) - ------------------------- - 4*\1 + cot (x)/*cot(x)*sin(2*x) - ------------------------- + ------------------------- + -------------------------|
| \ cot(x) / \ cot(x) / | 2 cot(x) | 2 3 cot(x) cot(x) |
\ \ cot (x) / cot (x) cot (x) /
$$\left(- \left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)}}{\cot{\left(x \right)}} - 2 \log{\left(\cot{\left(x \right)} \right)} \cos{\left(2 x \right)}\right)^{3} + 3 \left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)}}{\cot{\left(x \right)}} - 2 \log{\left(\cot{\left(x \right)} \right)} \cos{\left(2 x \right)}\right) \left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(2 x \right)}}{\cot^{2}{\left(x \right)}} - 2 \left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)} + \frac{4 \left(\cot^{2}{\left(x \right)} + 1\right) \cos{\left(2 x \right)}}{\cot{\left(x \right)}} + 4 \log{\left(\cot{\left(x \right)} \right)} \sin{\left(2 x \right)}\right) - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)^{3} \sin{\left(2 x \right)}}{\cot^{3}{\left(x \right)}} + \frac{4 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(2 x \right)}}{\cot{\left(x \right)}} - \frac{6 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cos{\left(2 x \right)}}{\cot^{2}{\left(x \right)}} - 4 \left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)} \cot{\left(x \right)} + \frac{12 \left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)}}{\cot{\left(x \right)}} + 12 \left(\cot^{2}{\left(x \right)} + 1\right) \cos{\left(2 x \right)} - 8 \log{\left(\cot{\left(x \right)} \right)} \cos{\left(2 x \right)}\right) \cot^{\sin{\left(2 x \right)}}{\left(x \right)}$$