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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of x*e^x
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Derivative of 2/x^3
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Derivative of acot(x)
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Derivative of arcsin(lnx)
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Identical expressions
- arcsin(lnx)
- arc sinus of (lnx)
- arcsinlnx
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Similar expressions
- y=arcsinlnx
- arcsin(ln(x))/ln(arcsin(x))
- arcsin(lnx^4+arctgx^2)+x^(1+x)
- -arcsin((lnx)/(sqrt(2)))+c
- xarcsin(ln(x))
Derivative of arcsin(lnx)
The solution
You have entered
[src]
asin(log(x))
$$\operatorname{asin}{\left(\log{\left(x \right)} \right)}$$
d --(asin(log(x))) dx
$$\frac{d}{d x} \operatorname{asin}{\left(\log{\left(x \right)} \right)}$$
The first derivative
[src]
1
------------------
_____________
/ 2
x*\/ 1 - log (x)
$$\frac{1}{x \sqrt{1 - \log{\left(x \right)}^{2}}}$$
The second derivative
[src]
log(x)
-1 + -----------
2
1 - log (x)
-------------------
_____________
2 / 2
x *\/ 1 - log (x)
$$\frac{-1 + \frac{\log{\left(x \right)}}{1 - \log{\left(x \right)}^{2}}}{x^{2} \sqrt{1 - \log{\left(x \right)}^{2}}}$$
The third derivative
[src]
2
1 3*log(x) 3*log (x)
2 + ----------- - ----------- + --------------
2 2 2
1 - log (x) 1 - log (x) / 2 \
\1 - log (x)/
----------------------------------------------
_____________
3 / 2
x *\/ 1 - log (x)
$$\frac{2 - \frac{3 \log{\left(x \right)}}{1 - \log{\left(x \right)}^{2}} + \frac{1}{1 - \log{\left(x \right)}^{2}} + \frac{3 \log{\left(x \right)}^{2}}{\left(1 - \log{\left(x \right)}^{2}\right)^{2}}}{x^{3} \sqrt{1 - \log{\left(x \right)}^{2}}}$$
The graph