Mister Exam
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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- Derivative of:
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Derivative of sin(x)+cos(x)
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Derivative of cos(x)^2
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Derivative of sin(x^3)
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Derivative of log(x)^2
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Identical expressions
- tg(two *x)^(cosx)
- tg(2 multiply by x) to the power of ( co sinus of e of x)
- tg(two multiply by x) to the power of ( co sinus of e of x)
- tg(2*x)(cosx)
- tg2*xcosx
- tg(2x)^(cosx)
- tg(2x)(cosx)
- tg2xcosx
- tg2x^cosx
Derivative of tg(2*x)^(cosx)
The solution
You have entered
[src]
cos(x) tan (2*x)
$$\tan^{\cos{\left(x \right)}}{\left(2 x \right)}$$
tan(2*x)^cos(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(x) | \2 + 2*tan (2*x)/*cos(x)|
tan (2*x)*|-log(tan(2*x))*sin(x) + ------------------------|
\ tan(2*x) /
$$\left(\frac{\left(2 \tan^{2}{\left(2 x \right)} + 2\right) \cos{\left(x \right)}}{\tan{\left(2 x \right)}} - \log{\left(\tan{\left(2 x \right)} \right)} \sin{\left(x \right)}\right) \tan^{\cos{\left(x \right)}}{\left(2 x \right)}$$
The second derivative
[src]
/ 2 2 \
|/ / 2 \ \ / 2 \ / 2 \ |
cos(x) || 2*\1 + tan (2*x)/*cos(x)| / 2 \ 4*\1 + tan (2*x)/ *cos(x) 4*\1 + tan (2*x)/*sin(x)|
tan (2*x)*||-log(tan(2*x))*sin(x) + ------------------------| - cos(x)*log(tan(2*x)) + 8*\1 + tan (2*x)/*cos(x) - ------------------------- - ------------------------|
|\ tan(2*x) / 2 tan(2*x) |
\ tan (2*x) /
$$\left(\left(\frac{2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cos{\left(x \right)}}{\tan{\left(2 x \right)}} - \log{\left(\tan{\left(2 x \right)} \right)} \sin{\left(x \right)}\right)^{2} - \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \cos{\left(x \right)}}{\tan^{2}{\left(2 x \right)}} - \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(2 x \right)}} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cos{\left(x \right)} - \log{\left(\tan{\left(2 x \right)} \right)} \cos{\left(x \right)}\right) \tan^{\cos{\left(x \right)}}{\left(2 x \right)}$$
The third derivative
[src]
/ 3 / 2 \ 2 2 3 \
|/ / 2 \ \ / / 2 \ \ | / 2 \ / 2 \ | / 2 \ / 2 \ / 2 \ / 2 \ |
cos(x) || 2*\1 + tan (2*x)/*cos(x)| / 2 \ | 2*\1 + tan (2*x)/*cos(x)| | / 2 \ 4*\1 + tan (2*x)/ *cos(x) 4*\1 + tan (2*x)/*sin(x)| 32*\1 + tan (2*x)/ *cos(x) 6*\1 + tan (2*x)/*cos(x) 12*\1 + tan (2*x)/ *sin(x) 16*\1 + tan (2*x)/ *cos(x) / 2 \ |
tan (2*x)*||-log(tan(2*x))*sin(x) + ------------------------| + log(tan(2*x))*sin(x) - 24*\1 + tan (2*x)/*sin(x) - 3*|-log(tan(2*x))*sin(x) + ------------------------|*|cos(x)*log(tan(2*x)) - 8*\1 + tan (2*x)/*cos(x) + ------------------------- + ------------------------| - -------------------------- - ------------------------ + -------------------------- + -------------------------- + 32*\1 + tan (2*x)/*cos(x)*tan(2*x)|
|\ tan(2*x) / \ tan(2*x) / | 2 tan(2*x) | tan(2*x) tan(2*x) 2 3 |
\ \ tan (2*x) / tan (2*x) tan (2*x) /
$$\left(\left(\frac{2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cos{\left(x \right)}}{\tan{\left(2 x \right)}} - \log{\left(\tan{\left(2 x \right)} \right)} \sin{\left(x \right)}\right)^{3} - 3 \left(\frac{2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cos{\left(x \right)}}{\tan{\left(2 x \right)}} - \log{\left(\tan{\left(2 x \right)} \right)} \sin{\left(x \right)}\right) \left(\frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \cos{\left(x \right)}}{\tan^{2}{\left(2 x \right)}} + \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(2 x \right)}} - 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cos{\left(x \right)} + \log{\left(\tan{\left(2 x \right)} \right)} \cos{\left(x \right)}\right) + \frac{16 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{3} \cos{\left(x \right)}}{\tan^{3}{\left(2 x \right)}} + \frac{12 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \sin{\left(x \right)}}{\tan^{2}{\left(2 x \right)}} - \frac{32 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \cos{\left(x \right)}}{\tan{\left(2 x \right)}} - 24 \left(\tan^{2}{\left(2 x \right)} + 1\right) \sin{\left(x \right)} + 32 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cos{\left(x \right)} \tan{\left(2 x \right)} - \frac{6 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cos{\left(x \right)}}{\tan{\left(2 x \right)}} + \log{\left(\tan{\left(2 x \right)} \right)} \sin{\left(x \right)}\right) \tan^{\cos{\left(x \right)}}{\left(2 x \right)}$$