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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 x^2/2x+1
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Derivative of log(t-1)
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Derivative of e^x/(1+x^2)
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Derivative of 8*cos(x)
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Identical expressions
- arcsin((x/ three)^(one / two))
- arc sinus of ((x divide by 3) to the power of (1 divide by 2))
- arc sinus of ((x divide by three) to the power of (one divide by two))
- arcsin((x/3)(1/2))
- arcsinx/31/2
- arcsinx/3^1/2
- arcsin((x divide by 3)^(1 divide by 2))
Derivative of arcsin((x/3)^(1/2))
The solution
You have entered
[src]
/ ___\
| / x |
asin| / - |
\\/ 3 /
$$\operatorname{asin}{\left(\sqrt{\frac{x}{3}} \right)}$$
asin(sqrt(x/3))
The first derivative
[src]
___
\/ 3
-------------------
_______
___ / x
6*\/ x * / 1 - -
\/ 3
$$\frac{\sqrt{3}}{6 \sqrt{x} \sqrt{- \frac{x}{3} + 1}}$$
The second derivative
[src]
___ / 1 3\
\/ 3 *|----- - -|
| x x|
|1 - - |
\ 3 /
--------------------
_______
___ / x
36*\/ x * / 1 - -
\/ 3
$$\frac{\sqrt{3} \left(\frac{1}{1 - \frac{x}{3}} - \frac{3}{x}\right)}{36 \sqrt{x} \sqrt{1 - \frac{x}{3}}}$$
The third derivative
[src]
___ / 1 9 2 \
\/ 3 *|-------- + -- - ---------|
| 2 2 / x\|
|/ x\ x x*|1 - -||
||1 - -| \ 3/|
\\ 3/ /
---------------------------------
_______
___ / x
72*\/ x * / 1 - -
\/ 3
$$\frac{\sqrt{3} \left(\frac{1}{\left(1 - \frac{x}{3}\right)^{2}} - \frac{2}{x \left(1 - \frac{x}{3}\right)} + \frac{9}{x^{2}}\right)}{72 \sqrt{x} \sqrt{1 - \frac{x}{3}}}$$