Mister Exam
Other calculators
- 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 (-2)/x^2
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Derivative of 2x^2-x
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Derivative of (cos(x))^sin(x)
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Derivative of y=3x^2
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Identical expressions
- (cos(x))^sin(x)
- ( co sinus of e of (x)) to the power of sinus of (x)
- (cos(x))sin(x)
- cosxsinx
- cosx^sinx
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Similar expressions
- cos(x)^sin(x)
- (cosx)^sinx
Derivative of (cos(x))^sin(x)
The solution
You have entered
[src]
sin(x) cos (x)
$$\cos^{\sin{\left(x \right)}}{\left(x \right)}$$
cos(x)^sin(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(x) | sin (x)|
cos (x)*|cos(x)*log(cos(x)) - -------|
\ cos(x)/
$$\left(\log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)} - \frac{\sin^{2}{\left(x \right)}}{\cos{\left(x \right)}}\right) \cos^{\sin{\left(x \right)}}{\left(x \right)}$$
The second derivative
[src]
/ 2 \
|/ 2 \ / 2 \ |
sin(x) || sin (x)| | sin (x) | |
cos (x)*||cos(x)*log(cos(x)) - -------| - |3 + ------- + log(cos(x))|*sin(x)|
|\ cos(x)/ | 2 | |
\ \ cos (x) / /
$$\left(\left(\log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)} - \frac{\sin^{2}{\left(x \right)}}{\cos{\left(x \right)}}\right)^{2} - \left(\log{\left(\cos{\left(x \right)} \right)} + \frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 3\right) \sin{\left(x \right)}\right) \cos^{\sin{\left(x \right)}}{\left(x \right)}$$
The third derivative
[src]
/ 3 \
|/ 2 \ 2 4 / 2 \ / 2 \ |
sin(x) || sin (x)| 2*sin (x) 2*sin (x) | sin (x)| | sin (x) | |
cos (x)*||cos(x)*log(cos(x)) - -------| - 3*cos(x) - cos(x)*log(cos(x)) - --------- - --------- - 3*|cos(x)*log(cos(x)) - -------|*|3 + ------- + log(cos(x))|*sin(x)|
|\ cos(x)/ cos(x) 3 \ cos(x)/ | 2 | |
\ cos (x) \ cos (x) / /
$$\left(\left(\log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)} - \frac{\sin^{2}{\left(x \right)}}{\cos{\left(x \right)}}\right)^{3} - 3 \left(\log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)} - \frac{\sin^{2}{\left(x \right)}}{\cos{\left(x \right)}}\right) \left(\log{\left(\cos{\left(x \right)} \right)} + \frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 3\right) \sin{\left(x \right)} - \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)} - \frac{2 \sin^{4}{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{2 \sin^{2}{\left(x \right)}}{\cos{\left(x \right)}} - 3 \cos{\left(x \right)}\right) \cos^{\sin{\left(x \right)}}{\left(x \right)}$$
The graph