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 4
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Derivative of 1/x^3
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Derivative of sin(x)^cos(x)
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Derivative of ctgx-1
- Limit of the function:
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sin(x)^cos(x)
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Identical expressions
- sin(x)^cos(x)
- sinus of (x) to the power of co sinus of e of (x)
- sin(x)cos(x)
- sinxcosx
- sinx^cosx
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Similar expressions
- (sin(x))^cos(x)
- (sinx)^cosx
- sinx^cosx
Derivative of sin(x)^cos(x)
The solution
You have entered
[src]
cos(x) sin (x)
$$\sin^{\cos{\left(x \right)}}{\left(x \right)}$$
sin(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) |cos (x) |
sin (x)*|------- - log(sin(x))*sin(x)|
\ sin(x) /
$$\left(- \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} + \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \sin^{\cos{\left(x \right)}}{\left(x \right)}$$
The second derivative
[src]
/ 2 \
|/ 2 \ / 2 \ |
cos(x) || cos (x)| | cos (x) | |
sin (x)*||log(sin(x))*sin(x) - -------| - |3 + ------- + log(sin(x))|*cos(x)|
|\ sin(x)/ | 2 | |
\ \ sin (x) / /
$$\left(\left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} - \left(\log{\left(\sin{\left(x \right)} \right)} + 3 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)}\right) \sin^{\cos{\left(x \right)}}{\left(x \right)}$$
The third derivative
[src]
/ 3 \
| / 2 \ 2 4 / 2 \ / 2 \ |
cos(x) | | cos (x)| 2*cos (x) 2*cos (x) | cos (x)| | cos (x) | |
sin (x)*|- |log(sin(x))*sin(x) - -------| + 3*sin(x) + log(sin(x))*sin(x) + --------- + --------- + 3*|log(sin(x))*sin(x) - -------|*|3 + ------- + log(sin(x))|*cos(x)|
| \ sin(x)/ sin(x) 3 \ sin(x)/ | 2 | |
\ sin (x) \ sin (x) / /
$$\left(- \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} + 3 \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(\log{\left(\sin{\left(x \right)} \right)} + 3 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)} + \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} + 3 \sin{\left(x \right)} + \frac{2 \cos^{2}{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \cos^{4}{\left(x \right)}}{\sin^{3}{\left(x \right)}}\right) \sin^{\cos{\left(x \right)}}{\left(x \right)}$$
The graph