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How to use it?
- Derivative of:
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Derivative of e^(sin(1-3*x)^(2))
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Derivative of x×ln(x)
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Derivative of x^3-48x+17
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Derivative of tg(x)^3
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Identical expressions
- x*arcsin(sqrt(x)/(x+ one))
- x multiply by arc sinus of ( square root of (x) divide by (x plus 1))
- x multiply by arc sinus of ( square root of (x) divide by (x plus one))
- x*arcsin(√(x)/(x+1))
- xarcsin(sqrt(x)/(x+1))
- xarcsinsqrtx/x+1
- x*arcsin(sqrt(x) divide by (x+1))
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Similar expressions
- x*arcsin(sqrt(x)/(x-1))
Derivative of x*arcsin(sqrt(x)/(x+1))
The solution
You have entered
[src]
/ ___\
|\/ x |
x*asin|-----|
\x + 1/
$$x \operatorname{asin}{\left(\frac{\sqrt{x}}{x + 1} \right)}$$
x*asin(sqrt(x)/(x + 1))
The first derivative
[src]
/ ___ \
| 1 \/ x |
x*|--------------- - --------|
| ___ 2| / ___\
\2*\/ x *(x + 1) (x + 1) / |\/ x |
------------------------------ + asin|-----|
______________ \x + 1/
/ x
/ 1 - --------
/ 2
\/ (x + 1)
$$\frac{x \left(- \frac{\sqrt{x}}{\left(x + 1\right)^{2}} + \frac{1}{2 \sqrt{x} \left(x + 1\right)}\right)}{\sqrt{- \frac{x}{\left(x + 1\right)^{2}} + 1}} + \operatorname{asin}{\left(\frac{\sqrt{x}}{x + 1} \right)}$$
The second derivative
[src]
/ / / ___\\\
| | / 2*x \ | 1 2*\/ x |||
| | |-1 + -----|*|- ----- + -------|||
| | ___ \ 1 + x/ | ___ 1 + x |||
| | 1 8*\/ x 4 \ \/ x /||
| x*|---- - -------- + ------------- + --------------------------------||
| | 3/2 2 ___ 2 / x \ ||
| |x (1 + x) \/ x *(1 + x) (1 + x) *|-1 + --------| ||
| ___ | | 2| ||
| 1 2*\/ x \ \ (1 + x) / /|
-|- ----- + ------- + ----------------------------------------------------------------------|
| ___ 1 + x 4 |
\ \/ x /
----------------------------------------------------------------------------------------------
______________
/ x
(1 + x)* / 1 - --------
/ 2
\/ (1 + x)
$$- \frac{\frac{2 \sqrt{x}}{x + 1} + \frac{x \left(- \frac{8 \sqrt{x}}{\left(x + 1\right)^{2}} + \frac{\left(\frac{2 \sqrt{x}}{x + 1} - \frac{1}{\sqrt{x}}\right) \left(\frac{2 x}{x + 1} - 1\right)}{\left(x + 1\right)^{2} \left(\frac{x}{\left(x + 1\right)^{2}} - 1\right)} + \frac{4}{\sqrt{x} \left(x + 1\right)} + \frac{1}{x^{\frac{3}{2}}}\right)}{4} - \frac{1}{\sqrt{x}}}{\left(x + 1\right) \sqrt{- \frac{x}{\left(x + 1\right)^{2}} + 1}}$$
The third derivative
[src]
/ 2 / ___\ / ___ \ / ___\\
| / 2*x \ | 1 2*\/ x | / 2*x \ | 1 8*\/ x 4 | / 3*x \ | 1 2*\/ x ||
| 3*|-1 + -----| *|- ----- + -------| 2*|-1 + -----|*|---- - -------- + -------------| 4*|-2 + -----|*|- ----- + -------||
| ___ \ 1 + x/ | ___ 1 + x | \ 1 + x/ | 3/2 2 ___ | \ 1 + x/ | ___ 1 + x ||
| 3 48*\/ x 6 24 \ \/ x / \x (1 + x) \/ x *(1 + x)/ \ \/ x /|
x*|---- - -------- + ------------ + -------------- - ----------------------------------- - ------------------------------------------------ + ----------------------------------|
| 5/2 3 3/2 ___ 2 2 2 / x \ 3 / x \ | / ___\
|x (1 + x) x *(1 + x) \/ x *(1 + x) 4 / x \ (1 + x) *|-1 + --------| (1 + x) *|-1 + --------| | / 2*x \ | 1 2*\/ x |
| (1 + x) *|-1 + --------| | 2| | 2| | 3*|-1 + -----|*|- ----- + -------|
___ | | 2| \ (1 + x) / \ (1 + x) / | \ 1 + x/ | ___ 1 + x |
3 3 6*\/ x \ \ (1 + x) / / \ \/ x /
- ------ - ------------- + -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------
3/2 ___ 2 8 2 / x \
4*x \/ x *(1 + x) (1 + x) 4*(1 + x) *|-1 + --------|
| 2|
\ (1 + x) /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
______________
/ x
(1 + x)* / 1 - --------
/ 2
\/ (1 + x)
$$\frac{\frac{6 \sqrt{x}}{\left(x + 1\right)^{2}} + \frac{x \left(- \frac{48 \sqrt{x}}{\left(x + 1\right)^{3}} - \frac{2 \left(\frac{2 x}{x + 1} - 1\right) \left(- \frac{8 \sqrt{x}}{\left(x + 1\right)^{2}} + \frac{4}{\sqrt{x} \left(x + 1\right)} + \frac{1}{x^{\frac{3}{2}}}\right)}{\left(x + 1\right)^{2} \left(\frac{x}{\left(x + 1\right)^{2}} - 1\right)} + \frac{4 \left(\frac{2 \sqrt{x}}{x + 1} - \frac{1}{\sqrt{x}}\right) \left(\frac{3 x}{x + 1} - 2\right)}{\left(x + 1\right)^{3} \left(\frac{x}{\left(x + 1\right)^{2}} - 1\right)} - \frac{3 \left(\frac{2 \sqrt{x}}{x + 1} - \frac{1}{\sqrt{x}}\right) \left(\frac{2 x}{x + 1} - 1\right)^{2}}{\left(x + 1\right)^{4} \left(\frac{x}{\left(x + 1\right)^{2}} - 1\right)^{2}} + \frac{24}{\sqrt{x} \left(x + 1\right)^{2}} + \frac{6}{x^{\frac{3}{2}} \left(x + 1\right)} + \frac{3}{x^{\frac{5}{2}}}\right)}{8} - \frac{3 \left(\frac{2 \sqrt{x}}{x + 1} - \frac{1}{\sqrt{x}}\right) \left(\frac{2 x}{x + 1} - 1\right)}{4 \left(x + 1\right)^{2} \left(\frac{x}{\left(x + 1\right)^{2}} - 1\right)} - \frac{3}{\sqrt{x} \left(x + 1\right)} - \frac{3}{4 x^{\frac{3}{2}}}}{\left(x + 1\right) \sqrt{- \frac{x}{\left(x + 1\right)^{2}} + 1}}$$