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 f(x)=4x^6+7x^5+1
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Derivative of cot(cos(2))+((sin(6*x)^(2))/cos(12*x))*(1/6)
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Derivative of (2*x+3)^5
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Derivative of x^-tan(x)
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Identical expressions
- sin5x^cos5x
- sinus of 5x to the power of co sinus of e of 5x
- sin5xcos5x
Derivative of sin5x^cos5x
The solution
You have entered
[src]
cos(5*x) sin (5*x)
$$\sin^{\cos{\left(5 x \right)}}{\left(5 x \right)}$$
sin(5*x)^cos(5*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(5*x) | 5*cos (5*x)|
sin (5*x)*|-5*log(sin(5*x))*sin(5*x) + -----------|
\ sin(5*x) /
$$\left(- 5 \log{\left(\sin{\left(5 x \right)} \right)} \sin{\left(5 x \right)} + \frac{5 \cos^{2}{\left(5 x \right)}}{\sin{\left(5 x \right)}}\right) \sin^{\cos{\left(5 x \right)}}{\left(5 x \right)}$$
The second derivative
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/ 2 \
|/ 2 \ / 2 \ |
cos(5*x) || cos (5*x)| | cos (5*x) | |
25*sin (5*x)*||log(sin(5*x))*sin(5*x) - ---------| - |3 + --------- + log(sin(5*x))|*cos(5*x)|
|\ sin(5*x)/ | 2 | |
\ \ sin (5*x) / /
$$25 \left(\left(\log{\left(\sin{\left(5 x \right)} \right)} \sin{\left(5 x \right)} - \frac{\cos^{2}{\left(5 x \right)}}{\sin{\left(5 x \right)}}\right)^{2} - \left(\log{\left(\sin{\left(5 x \right)} \right)} + 3 + \frac{\cos^{2}{\left(5 x \right)}}{\sin^{2}{\left(5 x \right)}}\right) \cos{\left(5 x \right)}\right) \sin^{\cos{\left(5 x \right)}}{\left(5 x \right)}$$
The third derivative
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/ 3 \
| / 2 \ 2 4 / 2 \ / 2 \ |
cos(5*x) | | cos (5*x)| 2*cos (5*x) 2*cos (5*x) | cos (5*x)| | cos (5*x) | |
125*sin (5*x)*|- |log(sin(5*x))*sin(5*x) - ---------| + 3*sin(5*x) + log(sin(5*x))*sin(5*x) + ----------- + ----------- + 3*|log(sin(5*x))*sin(5*x) - ---------|*|3 + --------- + log(sin(5*x))|*cos(5*x)|
| \ sin(5*x)/ sin(5*x) 3 \ sin(5*x)/ | 2 | |
\ sin (5*x) \ sin (5*x) / /
$$125 \left(- \left(\log{\left(\sin{\left(5 x \right)} \right)} \sin{\left(5 x \right)} - \frac{\cos^{2}{\left(5 x \right)}}{\sin{\left(5 x \right)}}\right)^{3} + 3 \left(\log{\left(\sin{\left(5 x \right)} \right)} \sin{\left(5 x \right)} - \frac{\cos^{2}{\left(5 x \right)}}{\sin{\left(5 x \right)}}\right) \left(\log{\left(\sin{\left(5 x \right)} \right)} + 3 + \frac{\cos^{2}{\left(5 x \right)}}{\sin^{2}{\left(5 x \right)}}\right) \cos{\left(5 x \right)} + \log{\left(\sin{\left(5 x \right)} \right)} \sin{\left(5 x \right)} + 3 \sin{\left(5 x \right)} + \frac{2 \cos^{2}{\left(5 x \right)}}{\sin{\left(5 x \right)}} + \frac{2 \cos^{4}{\left(5 x \right)}}{\sin^{3}{\left(5 x \right)}}\right) \sin^{\cos{\left(5 x \right)}}{\left(5 x \right)}$$