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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of (5*x-4)*(2*x^4-7*x+1)
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Derivative of x/5+5/x
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Derivative of (x+5)^2*(x-1)+7
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Derivative of x^3-48x+17
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Identical expressions
- (tgx)^sin2x
- (tgx) to the power of sinus of 2x
- (tgx)sin2x
- tgxsin2x
- tgx^sin2x
Derivative of (tgx)^sin2x
The solution
You have entered
[src]
sin(2*x) tan (x)
$$\tan^{\sin{\left(2 x \right)}}{\left(x \right)}$$
tan(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
[src]
/ / 2 \ \
sin(2*x) | \1 + tan (x)/*sin(2*x)|
tan (x)*|2*cos(2*x)*log(tan(x)) + ----------------------|
\ tan(x) /
$$\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)}}{\tan{\left(x \right)}} + 2 \log{\left(\tan{\left(x \right)} \right)} \cos{\left(2 x \right)}\right) \tan^{\sin{\left(2 x \right)}}{\left(x \right)}$$
The second derivative
[src]
/ 2 2 \
|/ / 2 \ \ / 2 \ / 2 \ |
sin(2*x) || \1 + tan (x)/*sin(2*x)| / 2 \ \1 + tan (x)/ *sin(2*x) 4*\1 + tan (x)/*cos(2*x)|
tan (x)*||2*cos(2*x)*log(tan(x)) + ----------------------| - 4*log(tan(x))*sin(2*x) + 2*\1 + tan (x)/*sin(2*x) - ----------------------- + ------------------------|
|\ tan(x) / 2 tan(x) |
\ tan (x) /
$$\left(\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)}}{\tan{\left(x \right)}} + 2 \log{\left(\tan{\left(x \right)} \right)} \cos{\left(2 x \right)}\right)^{2} - \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(2 x \right)}}{\tan^{2}{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)} + \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(2 x \right)}}{\tan{\left(x \right)}} - 4 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(2 x \right)}\right) \tan^{\sin{\left(2 x \right)}}{\left(x \right)}$$
The third derivative
[src]
/ 3 / 2 \ 2 2 3 \
|/ / 2 \ \ / / 2 \ \ | / 2 \ / 2 \ | / 2 \ / 2 \ / 2 \ / 2 \ |
sin(2*x) || \1 + tan (x)/*sin(2*x)| | \1 + tan (x)/*sin(2*x)| | / 2 \ \1 + tan (x)/ *sin(2*x) 4*\1 + tan (x)/*cos(2*x)| / 2 \ 12*\1 + tan (x)/*sin(2*x) 6*\1 + tan (x)/ *cos(2*x) 4*\1 + tan (x)/ *sin(2*x) 2*\1 + tan (x)/ *sin(2*x) / 2 \ |
tan (x)*||2*cos(2*x)*log(tan(x)) + ----------------------| - 8*cos(2*x)*log(tan(x)) - 3*|2*cos(2*x)*log(tan(x)) + ----------------------|*|- 2*\1 + tan (x)/*sin(2*x) + 4*log(tan(x))*sin(2*x) + ----------------------- - ------------------------| + 12*\1 + tan (x)/*cos(2*x) - ------------------------- - ------------------------- - ------------------------- + ------------------------- + 4*\1 + tan (x)/*sin(2*x)*tan(x)|
|\ tan(x) / \ tan(x) / | 2 tan(x) | tan(x) 2 tan(x) 3 |
\ \ tan (x) / tan (x) tan (x) /
$$\left(\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)}}{\tan{\left(x \right)}} + 2 \log{\left(\tan{\left(x \right)} \right)} \cos{\left(2 x \right)}\right)^{3} - 3 \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)}}{\tan{\left(x \right)}} + 2 \log{\left(\tan{\left(x \right)} \right)} \cos{\left(2 x \right)}\right) \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(2 x \right)}}{\tan^{2}{\left(x \right)}} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(2 x \right)}}{\tan{\left(x \right)}} + 4 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(2 x \right)}\right) + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{3} \sin{\left(2 x \right)}}{\tan^{3}{\left(x \right)}} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(2 x \right)}}{\tan{\left(x \right)}} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \cos{\left(2 x \right)}}{\tan^{2}{\left(x \right)}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)} \tan{\left(x \right)} - \frac{12 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(2 x \right)}}{\tan{\left(x \right)}} + 12 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(2 x \right)} - 8 \log{\left(\tan{\left(x \right)} \right)} \cos{\left(2 x \right)}\right) \tan^{\sin{\left(2 x \right)}}{\left(x \right)}$$
The graph