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 16/x
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Derivative of e^(sin(1-3*x)^(2))
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Derivative of (1+x)/(4-x^2)
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Derivative of 2*sqrt(x^3)
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Identical expressions
- (cot(x)/ two)^tan(two *x)
- ( cotangent of (x) divide by 2) to the power of tangent of (2 multiply by x)
- ( cotangent of (x) divide by two) to the power of tangent of (two multiply by x)
- (cot(x)/2)tan(2*x)
- cotx/2tan2*x
- (cot(x)/2)^tan(2x)
- (cot(x)/2)tan(2x)
- cotx/2tan2x
- cotx/2^tan2x
- (cot(x) divide by 2)^tan(2*x)
Derivative of (cot(x)/2)^tan(2*x)
The solution
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[src]
tan(2*x) /cot(x)\ |------| \ 2 /
$$\left(\frac{\cot{\left(x \right)}}{2}\right)^{\tan{\left(2 x \right)}}$$
(cot(x)/2)^tan(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 \ \
| | 1 cot (x)| |
tan(2*x) | 2*|- - - -------|*tan(2*x)|
/cot(x)\ |/ 2 \ /cot(x)\ \ 2 2 / |
|------| *|\2 + 2*tan (2*x)/*log|------| + --------------------------|
\ 2 / \ \ 2 / cot(x) /
$$\left(\frac{\cot{\left(x \right)}}{2}\right)^{\tan{\left(2 x \right)}} \left(\left(2 \tan^{2}{\left(2 x \right)} + 2\right) \log{\left(\frac{\cot{\left(x \right)}}{2} \right)} + \frac{2 \left(- \frac{\cot^{2}{\left(x \right)}}{2} - \frac{1}{2}\right) \tan{\left(2 x \right)}}{\cot{\left(x \right)}}\right)$$
The second derivative
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/ 2 2 \
tan(2*x) |/ / 2 \ \ / 2 \ / 2 \ / 2 \ |
/cot(x)\ || / 2 \ /cot(x)\ \1 + cot (x)/*tan(2*x)| / 2 \ \1 + cot (x)/ *tan(2*x) 4*\1 + cot (x)/*\1 + tan (2*x)/ / 2 \ /cot(x)\ |
|------| *||2*\1 + tan (2*x)/*log|------| - ----------------------| + 2*\1 + cot (x)/*tan(2*x) - ----------------------- - ------------------------------- + 8*\1 + tan (2*x)/*log|------|*tan(2*x)|
\ 2 / |\ \ 2 / cot(x) / 2 cot(x) \ 2 / |
\ cot (x) /
$$\left(\frac{\cot{\left(x \right)}}{2}\right)^{\tan{\left(2 x \right)}} \left(\left(2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(\frac{\cot{\left(x \right)}}{2} \right)} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(2 x \right)}}{\cot{\left(x \right)}}\right)^{2} - \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(\frac{\cot{\left(x \right)}}{2} \right)} \tan{\left(2 x \right)} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(2 x \right)}}{\cot^{2}{\left(x \right)}} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(2 x \right)}\right)$$
The third derivative
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/ 3 / 2 \ 2 3 2 \
tan(2*x) |/ / 2 \ \ / / 2 \ \ | / 2 \ / 2 \ / 2 \| 2 / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ |
/cot(x)\ || / 2 \ /cot(x)\ \1 + cot (x)/*tan(2*x)| | / 2 \ /cot(x)\ \1 + cot (x)/*tan(2*x)| | / 2 \ \1 + cot (x)/ *tan(2*x) / 2 \ /cot(x)\ 4*\1 + cot (x)/*\1 + tan (2*x)/| / 2 \ / 2 \ / 2 \ /cot(x)\ 6*\1 + cot (x)/ *\1 + tan (2*x)/ / 2 \ 2*\1 + cot (x)/ *tan(2*x) 4*\1 + cot (x)/ *tan(2*x) 2 / 2 \ /cot(x)\ 24*\1 + cot (x)/*\1 + tan (2*x)/*tan(2*x)|
|------| *||2*\1 + tan (2*x)/*log|------| - ----------------------| - 3*|2*\1 + tan (2*x)/*log|------| - ----------------------|*|- 2*\1 + cot (x)/*tan(2*x) + ----------------------- - 8*\1 + tan (2*x)/*log|------|*tan(2*x) + -------------------------------| + 12*\1 + cot (x)/*\1 + tan (2*x)/ + 16*\1 + tan (2*x)/ *log|------| - -------------------------------- - 4*\1 + cot (x)/*cot(x)*tan(2*x) - ------------------------- + ------------------------- + 32*tan (2*x)*\1 + tan (2*x)/*log|------| - -----------------------------------------|
\ 2 / |\ \ 2 / cot(x) / \ \ 2 / cot(x) / | 2 \ 2 / cot(x) | \ 2 / 2 3 cot(x) \ 2 / cot(x) |
\ \ cot (x) / cot (x) cot (x) /
$$\left(\frac{\cot{\left(x \right)}}{2}\right)^{\tan{\left(2 x \right)}} \left(\left(2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(\frac{\cot{\left(x \right)}}{2} \right)} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(2 x \right)}}{\cot{\left(x \right)}}\right)^{3} - 3 \left(2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(\frac{\cot{\left(x \right)}}{2} \right)} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(2 x \right)}}{\cot{\left(x \right)}}\right) \left(\frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(\frac{\cot{\left(x \right)}}{2} \right)} \tan{\left(2 x \right)} + \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(2 x \right)}}{\cot^{2}{\left(x \right)}} - 2 \left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(2 x \right)}\right) + 16 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \log{\left(\frac{\cot{\left(x \right)}}{2} \right)} - \frac{6 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\cot^{2}{\left(x \right)}} - \frac{24 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(2 x \right)}}{\cot{\left(x \right)}} + 12 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right) + 32 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(\frac{\cot{\left(x \right)}}{2} \right)} \tan^{2}{\left(2 x \right)} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)^{3} \tan{\left(2 x \right)}}{\cot^{3}{\left(x \right)}} + \frac{4 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(2 x \right)}}{\cot{\left(x \right)}} - 4 \left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(2 x \right)} \cot{\left(x \right)}\right)$$