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
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- 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 arctg(1/x)
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Derivative of e^cos(x)
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Derivative of ln(x+3)^3
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Derivative of cot(1/x)
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Identical expressions
- sin(x)^log(x)
- sinus of (x) to the power of logarithm of (x)
- sin(x)log(x)
- sinxlogx
- sinx^logx
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Similar expressions
- sinx^log(x)
Derivative of sin(x)^log(x)
The solution
You have entered
[src]
log(x) sin (x)
$$\sin^{\log{\left(x \right)}}{\left(x \right)}$$
sin(x)^log(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]
log(x) /log(sin(x)) cos(x)*log(x)\
sin (x)*|----------- + -------------|
\ x sin(x) /
$$\left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{x}\right) \sin^{\log{\left(x \right)}}{\left(x \right)}$$
The second derivative
[src]
/ 2 2 \
log(x) |/log(sin(x)) cos(x)*log(x)\ log(sin(x)) cos (x)*log(x) 2*cos(x)|
sin (x)*||----------- + -------------| - log(x) - ----------- - -------------- + --------|
|\ x sin(x) / 2 2 x*sin(x)|
\ x sin (x) /
$$\left(\left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{x}\right)^{2} - \log{\left(x \right)} - \frac{\log{\left(x \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{2 \cos{\left(x \right)}}{x \sin{\left(x \right)}} - \frac{\log{\left(\sin{\left(x \right)} \right)}}{x^{2}}\right) \sin^{\log{\left(x \right)}}{\left(x \right)}$$
The third derivative
[src]
/ 3 / 2 \ 2 3 \
log(x) |/log(sin(x)) cos(x)*log(x)\ 3 /log(sin(x)) cos(x)*log(x)\ |log(sin(x)) cos (x)*log(x) 2*cos(x) | 2*log(sin(x)) 3*cos (x) 3*cos(x) 2*cos (x)*log(x) 2*cos(x)*log(x)|
sin (x)*||----------- + -------------| - - - 3*|----------- + -------------|*|----------- + -------------- - -------- + log(x)| + ------------- - --------- - --------- + ---------------- + ---------------|
|\ x sin(x) / x \ x sin(x) / | 2 2 x*sin(x) | 3 2 2 3 sin(x) |
\ \ x sin (x) / x x*sin (x) x *sin(x) sin (x) /
$$\left(\left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{x}\right)^{3} - 3 \left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{x}\right) \left(\log{\left(x \right)} + \frac{\log{\left(x \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{x \sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{x^{2}}\right) + \frac{2 \log{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \log{\left(x \right)} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - \frac{3}{x} - \frac{3 \cos^{2}{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{3 \cos{\left(x \right)}}{x^{2} \sin{\left(x \right)}} + \frac{2 \log{\left(\sin{\left(x \right)} \right)}}{x^{3}}\right) \sin^{\log{\left(x \right)}}{\left(x \right)}$$