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 (2x-1)^3
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Derivative of 2*cos(3*x)
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Derivative of x^2/(x^2+1)
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Derivative of (x+1)/(x^2+1)
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Identical expressions
- lnx^sinx
- lnx to the power of sinus of x
- lnxsinx
Derivative of lnx^sinx
The solution
You have entered
[src]
sin(x) log (x)
$$\log{\left(x \right)}^{\sin{\left(x \right)}}$$
d / sin(x) \ --\log (x)/ dx
$$\frac{d}{d x} \log{\left(x \right)}^{\sin{\left(x \right)}}$$
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]
sin(x) / sin(x) \
log (x)*|cos(x)*log(log(x)) + --------|
\ x*log(x)/
$$\left(\log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{\sin{\left(x \right)}}$$
The second derivative
[src]
/ 2 \
sin(x) |/ sin(x) \ sin(x) sin(x) 2*cos(x)|
log (x)*||cos(x)*log(log(x)) + --------| - log(log(x))*sin(x) - --------- - ---------- + --------|
|\ x*log(x)/ 2 2 2 x*log(x)|
\ x *log(x) x *log (x) /
$$\left(\left(\log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x \log{\left(x \right)}}\right)^{2} - \log{\left(\log{\left(x \right)} \right)} \sin{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x \log{\left(x \right)}} - \frac{\sin{\left(x \right)}}{x^{2} \log{\left(x \right)}} - \frac{\sin{\left(x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) \log{\left(x \right)}^{\sin{\left(x \right)}}$$
The third derivative
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/ 3 \
sin(x) |/ sin(x) \ / sin(x) \ / sin(x) sin(x) 2*cos(x)\ 3*sin(x) 3*cos(x) 3*cos(x) 2*sin(x) 2*sin(x) 3*sin(x) |
log (x)*||cos(x)*log(log(x)) + --------| - cos(x)*log(log(x)) - 3*|cos(x)*log(log(x)) + --------|*|log(log(x))*sin(x) + --------- + ---------- - --------| - -------- - --------- - ---------- + --------- + ---------- + ----------|
|\ x*log(x)/ \ x*log(x)/ | 2 2 2 x*log(x)| x*log(x) 2 2 2 3 3 3 3 2 |
\ \ x *log(x) x *log (x) / x *log(x) x *log (x) x *log(x) x *log (x) x *log (x)/
$$\left(\left(\log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x \log{\left(x \right)}}\right)^{3} - 3 \left(\log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x \log{\left(x \right)}}\right) \left(\log{\left(\log{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x \log{\left(x \right)}} + \frac{\sin{\left(x \right)}}{x^{2} \log{\left(x \right)}} + \frac{\sin{\left(x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) - \log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} - \frac{3 \sin{\left(x \right)}}{x \log{\left(x \right)}} - \frac{3 \cos{\left(x \right)}}{x^{2} \log{\left(x \right)}} - \frac{3 \cos{\left(x \right)}}{x^{2} \log{\left(x \right)}^{2}} + \frac{2 \sin{\left(x \right)}}{x^{3} \log{\left(x \right)}} + \frac{3 \sin{\left(x \right)}}{x^{3} \log{\left(x \right)}^{2}} + \frac{2 \sin{\left(x \right)}}{x^{3} \log{\left(x \right)}^{3}}\right) \log{\left(x \right)}^{\sin{\left(x \right)}}$$
The graph