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 sin(x)/(1+cos(x))
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Derivative of f(x)=x
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Derivative of ln(lnx)
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Derivative of f
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Identical expressions
- arcsinx*lnx
- arc sinus of x multiply by lnx
- arcsinxlnx
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Similar expressions
- 4arcsinxlnx-2/x
- y=arcsinxlnx
- arcsin(x)*ln(x^2-exp^x)
Derivative of arcsinx*lnx
The solution
You have entered
[src]
asin(x)*log(x)
$$\log{\left(x \right)} \operatorname{asin}{\left(x \right)}$$
asin(x)*log(x)
The first derivative
[src]
asin(x) log(x)
------- + -----------
x ________
/ 2
\/ 1 - x
$$\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{x}$$
The second derivative
[src]
asin(x) 2 x*log(x)
- ------- + ------------- + -----------
2 ________ 3/2
x / 2 / 2\
x*\/ 1 - x \1 - x /
$$\frac{x \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{x \sqrt{1 - x^{2}}} - \frac{\operatorname{asin}{\left(x \right)}}{x^{2}}$$
The third derivative
[src]
/ 2 \
| 3*x |
|-1 + -------|*log(x)
| 2|
3 3 2*asin(x) \ -1 + x /
----------- - -------------- + --------- - ---------------------
3/2 ________ 3 3/2
/ 2\ 2 / 2 x / 2\
\1 - x / x *\/ 1 - x \1 - x /
$$- \frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{3}{x^{2} \sqrt{1 - x^{2}}} + \frac{2 \operatorname{asin}{\left(x \right)}}{x^{3}}$$