Mister Exam
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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 e^(5*x)
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Derivative of x^2+x+1
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Derivative of (x^2+1)^2
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Derivative of sqrt(2*x)
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Identical expressions
- arcsin(sqrt(x/(x+ one)))
- arc sinus of ( square root of (x divide by (x plus 1)))
- arc sinus of ( square root of (x divide by (x plus one)))
- arcsin(√(x/(x+1)))
- arcsinsqrtx/x+1
- arcsin(sqrt(x divide by (x+1)))
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Similar expressions
- x*arcsin(sqrt(x)/(x+1))
- arcsin(sqrt(x/(x-1)))
Derivative of arcsin(sqrt(x/(x+1)))
The solution
You have entered
[src]
/ _______\
| / x |
asin| / ----- |
\\/ x + 1 /
$$\operatorname{asin}{\left(\sqrt{\frac{x}{x + 1}} \right)}$$
/ / _______\\ d | | / x || --|asin| / ----- || dx\ \\/ x + 1 //
$$\frac{d}{d x} \operatorname{asin}{\left(\sqrt{\frac{x}{x + 1}} \right)}$$
The first derivative
[src]
_______
/ x / 1 x \
/ ----- *(x + 1)*|--------- - ----------|
\/ x + 1 |2*(x + 1) 2|
\ 2*(x + 1) /
--------------------------------------------
___________
/ x
x* / 1 - -----
\/ x + 1
$$\frac{\sqrt{\frac{x}{x + 1}} \left(x + 1\right) \left(- \frac{x}{2 \left(x + 1\right)^{2}} + \frac{1}{2 \left(x + 1\right)}\right)}{x \sqrt{- \frac{x}{x + 1} + 1}}$$
The second derivative
[src]
/ x x \
_______ | -1 + ----- -1 + ----- |
/ x / x \ |2 2 1 + x 1 + x |
/ ----- *|-1 + -----|*|- + ----- + ---------- + -------------------|
\/ 1 + x \ 1 + x/ |x 1 + x x / x \|
| (1 + x)*|1 - -----||
\ \ 1 + x//
-----------------------------------------------------------------------
___________
/ x
4*x* / 1 - -----
\/ 1 + x
$$\frac{\sqrt{\frac{x}{x + 1}} \left(\frac{x}{x + 1} - 1\right) \left(\frac{\frac{x}{x + 1} - 1}{x} + \frac{2}{x + 1} + \frac{\frac{x}{x + 1} - 1}{\left(x + 1\right) \left(- \frac{x}{x + 1} + 1\right)} + \frac{2}{x}\right)}{4 x \sqrt{- \frac{x}{x + 1} + 1}}$$
The third derivative
[src]
/ 2 2 2 \
| / x \ / x \ x / x \ / x \ x / x \ |
_______ | 3*|-1 + -----| |-1 + -----| -1 + ----- 3*|-1 + -----| 3*|-1 + -----| -1 + ----- |-1 + -----| |
/ x / x \ | 1 1 1 \ 1 + x/ \ 1 + x/ 1 + x \ 1 + x/ \ 1 + x/ 1 + x \ 1 + x/ |
/ ----- *|-1 + -----|*|- -- - -------- - --------- - -------------- - ------------- - -------------------- - -------------- - ----------------------- - ----------------------- - -----------------------|
\/ 1 + x \ 1 + x/ | 2 2 x*(1 + x) 2 2 2 / x \ 4*x*(1 + x) 2 / x \ / x \|
| x (1 + x) 4*x 8*x (1 + x) *|1 - -----| 2 / x \ 2*x*(1 + x)*|1 - -----| 4*x*(1 + x)*|1 - -----||
| \ 1 + x/ 8*(1 + x) *|1 - -----| \ 1 + x/ \ 1 + x/|
\ \ 1 + x/ /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
___________
/ x
x* / 1 - -----
\/ 1 + x
$$\frac{\sqrt{\frac{x}{x + 1}} \left(\frac{x}{x + 1} - 1\right) \left(- \frac{\left(\frac{x}{x + 1} - 1\right)^{2}}{8 x^{2}} - \frac{3 \left(\frac{x}{x + 1} - 1\right)}{4 x \left(x + 1\right)} - \frac{\left(\frac{x}{x + 1} - 1\right)^{2}}{4 x \left(x + 1\right) \left(- \frac{x}{x + 1} + 1\right)} - \frac{3 \left(\frac{x}{x + 1} - 1\right)}{4 x^{2}} - \frac{1}{\left(x + 1\right)^{2}} - \frac{\frac{x}{x + 1} - 1}{\left(x + 1\right)^{2} \left(- \frac{x}{x + 1} + 1\right)} - \frac{3 \left(\frac{x}{x + 1} - 1\right)^{2}}{8 \left(x + 1\right)^{2} \left(- \frac{x}{x + 1} + 1\right)^{2}} - \frac{1}{x \left(x + 1\right)} - \frac{\frac{x}{x + 1} - 1}{2 x \left(x + 1\right) \left(- \frac{x}{x + 1} + 1\right)} - \frac{1}{x^{2}}\right)}{x \sqrt{- \frac{x}{x + 1} + 1}}$$
The graph