Mister Exam
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- Derivative of a implicit defined function
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- Partial derivative of the function
- Curve tracing functions Step by Step
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- Differential equations Step by Step
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How to use it?
- Derivative of:
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Derivative of x^12
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Derivative of -e^x
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Derivative of e^(2-x)
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Derivative of x^2-4*x
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Identical expressions
- x^sin^-1x
- x to the power of sinus of to the power of minus 1x
- xsin-1x
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Similar expressions
- x^sin^+1x
Derivative of x^sin^-1x
The solution
You have entered
[src]
1 ------ sin(x) x
$$x^{\frac{1}{\sin{\left(x \right)}}}$$
/ 1 \ | ------| d | sin(x)| --\x / dx
$$\frac{d}{d x} x^{\frac{1}{\sin{\left(x \right)}}}$$
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]
1
------
sin(x) / 1 cos(x)*log(x)\
x *|-------- - -------------|
|x*sin(x) 2 |
\ sin (x) /
$$x^{\frac{1}{\sin{\left(x \right)}}} \left(- \frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{1}{x \sin{\left(x \right)}}\right)$$
The second derivative
[src]
/ 2 \
1 | / 1 cos(x)*log(x)\ |
------ | |- - + -------------| 2 |
sin(x) | 1 \ x sin(x) / 2*cos(x) 2*cos (x)*log(x) |
x *|- -- + ---------------------- - -------- + ---------------- + log(x)|
| 2 sin(x) x*sin(x) 2 |
\ x sin (x) /
------------------------------------------------------------------------------
sin(x)
$$\frac{x^{\frac{1}{\sin{\left(x \right)}}} \left(\frac{\left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{1}{x}\right)^{2}}{\sin{\left(x \right)}} + \log{\left(x \right)} + \frac{2 \log{\left(x \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{x \sin{\left(x \right)}} - \frac{1}{x^{2}}\right)}{\sin{\left(x \right)}}$$
The third derivative
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/ / 2 \ \
| 3 / 1 cos(x)*log(x)\ | 1 2*cos(x) 2*cos (x)*log(x) | |
1 | / 1 cos(x)*log(x)\ 3*|- - + -------------|*|- -- - -------- + ---------------- + log(x)| |
------ | |- - + -------------| 3 \ x sin(x) / | 2 x*sin(x) 2 | 2 |
sin(x) |2 3 \ x sin(x) / 6*cos (x)*log(x) 5*cos(x)*log(x) \ x sin (x) / 3*cos(x) 6*cos (x)|
x *|-- + - - ---------------------- - ---------------- - --------------- - --------------------------------------------------------------------- + --------- + ---------|
| 3 x 2 3 sin(x) sin(x) 2 2 |
\x sin (x) sin (x) x *sin(x) x*sin (x)/
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
sin(x)
$$\frac{x^{\frac{1}{\sin{\left(x \right)}}} \left(- \frac{\left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{1}{x}\right)^{3}}{\sin^{2}{\left(x \right)}} - \frac{3 \left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{1}{x}\right) \left(\log{\left(x \right)} + \frac{2 \log{\left(x \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{x \sin{\left(x \right)}} - \frac{1}{x^{2}}\right)}{\sin{\left(x \right)}} - \frac{5 \log{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{6 \log{\left(x \right)} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} + \frac{3}{x} + \frac{6 \cos^{2}{\left(x \right)}}{x \sin^{2}{\left(x \right)}} + \frac{3 \cos{\left(x \right)}}{x^{2} \sin{\left(x \right)}} + \frac{2}{x^{3}}\right)}{\sin{\left(x \right)}}$$
The graph