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 6^x
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Derivative of (x+3)^4
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Derivative of x^2+3x
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Derivative of log10(x)
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Identical expressions
- z=arcsiny*lny
- z equally arc sinus of y multiply by lny
- z=arcsinylny
Derivative of z=arcsiny*lny
The solution
You have entered
[src]
asin(y)*log(y)
$$\log{\left(y \right)} \operatorname{asin}{\left(y \right)}$$
asin(y)*log(y)
The first derivative
[src]
asin(y) log(y)
------- + -----------
y ________
/ 2
\/ 1 - y
$$\frac{\log{\left(y \right)}}{\sqrt{1 - y^{2}}} + \frac{\operatorname{asin}{\left(y \right)}}{y}$$
The second derivative
[src]
asin(y) 2 y*log(y)
- ------- + ------------- + -----------
2 ________ 3/2
y / 2 / 2\
y*\/ 1 - y \1 - y /
$$\frac{y \log{\left(y \right)}}{\left(1 - y^{2}\right)^{\frac{3}{2}}} + \frac{2}{y \sqrt{1 - y^{2}}} - \frac{\operatorname{asin}{\left(y \right)}}{y^{2}}$$
The third derivative
[src]
/ 2 \
| 3*y |
|-1 + -------|*log(y)
| 2|
3 3 2*asin(y) \ -1 + y /
----------- - -------------- + --------- - ---------------------
3/2 ________ 3 3/2
/ 2\ 2 / 2 y / 2\
\1 - y / y *\/ 1 - y \1 - y /
$$- \frac{\left(\frac{3 y^{2}}{y^{2} - 1} - 1\right) \log{\left(y \right)}}{\left(1 - y^{2}\right)^{\frac{3}{2}}} + \frac{3}{\left(1 - y^{2}\right)^{\frac{3}{2}}} - \frac{3}{y^{2} \sqrt{1 - y^{2}}} + \frac{2 \operatorname{asin}{\left(y \right)}}{y^{3}}$$
The graph