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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 y=2x+3
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Derivative of ln(x+5)^5
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Derivative of (3-2*x)*cos(x)
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Derivative of x^3-x+3
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Identical expressions
- y=(sin2x)^cos2x
- y equally ( sinus of 2x) to the power of co sinus of e of 2x
- y=(sin2x)cos2x
- y=sin2xcos2x
- y=sin2x^cos2x
Derivative of y=(sin2x)^cos2x
The solution
You have entered
[src]
cos(2*x) sin (2*x)
$$\sin^{\cos{\left(2 x \right)}}{\left(2 x \right)}$$
sin(2*x)^cos(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 \
cos(2*x) | 2*cos (2*x)|
sin (2*x)*|-2*log(sin(2*x))*sin(2*x) + -----------|
\ sin(2*x) /
$$\left(- 2 \log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(2 x \right)} + \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)}}\right) \sin^{\cos{\left(2 x \right)}}{\left(2 x \right)}$$
The second derivative
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/ 2 \
|/ 2 \ / 2 \ |
cos(2*x) || cos (2*x)| | cos (2*x) | |
4*sin (2*x)*||log(sin(2*x))*sin(2*x) - ---------| - |3 + --------- + log(sin(2*x))|*cos(2*x)|
|\ sin(2*x)/ | 2 | |
\ \ sin (2*x) / /
$$4 \left(\left(\log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(2 x \right)} - \frac{\cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)}}\right)^{2} - \left(\log{\left(\sin{\left(2 x \right)} \right)} + 3 + \frac{\cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}}\right) \cos{\left(2 x \right)}\right) \sin^{\cos{\left(2 x \right)}}{\left(2 x \right)}$$
The third derivative
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/ 3 \
| / 2 \ 2 4 / 2 \ / 2 \ |
cos(2*x) | | cos (2*x)| 2*cos (2*x) 2*cos (2*x) | cos (2*x)| | cos (2*x) | |
8*sin (2*x)*|- |log(sin(2*x))*sin(2*x) - ---------| + 3*sin(2*x) + log(sin(2*x))*sin(2*x) + ----------- + ----------- + 3*|log(sin(2*x))*sin(2*x) - ---------|*|3 + --------- + log(sin(2*x))|*cos(2*x)|
| \ sin(2*x)/ sin(2*x) 3 \ sin(2*x)/ | 2 | |
\ sin (2*x) \ sin (2*x) / /
$$8 \left(- \left(\log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(2 x \right)} - \frac{\cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)}}\right)^{3} + 3 \left(\log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(2 x \right)} - \frac{\cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)}}\right) \left(\log{\left(\sin{\left(2 x \right)} \right)} + 3 + \frac{\cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}}\right) \cos{\left(2 x \right)} + \log{\left(\sin{\left(2 x \right)} \right)} \sin{\left(2 x \right)} + 3 \sin{\left(2 x \right)} + \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)}} + \frac{2 \cos^{4}{\left(2 x \right)}}{\sin^{3}{\left(2 x \right)}}\right) \sin^{\cos{\left(2 x \right)}}{\left(2 x \right)}$$
The graph