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How to use it?
- Derivative of:
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Derivative of x^6/6
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Derivative of y=5x-6
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Derivative of x*log(x)-x
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Derivative of x^6+x-1/x^2
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Identical expressions
- arcsin(sqrt(x)/(x- five))
- arc sinus of ( square root of (x) divide by (x minus 5))
- arc sinus of ( square root of (x) divide by (x minus five))
- arcsin(√(x)/(x-5))
- arcsinsqrtx/x-5
- arcsin(sqrt(x) divide by (x-5))
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Similar expressions
- arcsin(sqrt(x)/(x+5))
Derivative of arcsin(sqrt(x)/(x-5))
The solution
You have entered
[src]
/ ___\
|\/ x |
asin|-----|
\x - 5/
$$\operatorname{asin}{\left(\frac{\sqrt{x}}{x - 5} \right)}$$
The first derivative
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___
1 \/ x
--------------- - --------
___ 2
2*\/ x *(x - 5) (x - 5)
--------------------------
______________
/ x
/ 1 - --------
/ 2
\/ (x - 5)
$$\frac{- \frac{\sqrt{x}}{\left(x - 5\right)^{2}} + \frac{1}{2 \sqrt{x} \left(x - 5\right)}}{\sqrt{- \frac{x}{\left(x - 5\right)^{2}} + 1}}$$
The second derivative
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/ ___\
/ 2*x \ | 1 2*\/ x |
|-1 + ------|*|- ----- + -------|
___ \ -5 + x/ | ___ -5 + x|
1 1 2*\/ x \ \/ x /
- ------ - -------------- + --------- + ---------------------------------
3/2 ___ 2 / x \ 2
4*x \/ x *(-5 + x) (-5 + x) 4*|1 - ---------|*(-5 + x)
| 2|
\ (-5 + x) /
-------------------------------------------------------------------------
_______________
/ x
/ 1 - --------- *(-5 + x)
/ 2
\/ (-5 + x)
$$\frac{\frac{2 \sqrt{x}}{\left(x - 5\right)^{2}} + \frac{\left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right) \left(\frac{2 x}{x - 5} - 1\right)}{4 \left(x - 5\right)^{2} \left(- \frac{x}{\left(x - 5\right)^{2}} + 1\right)} - \frac{1}{\sqrt{x} \left(x - 5\right)} - \frac{1}{4 x^{\frac{3}{2}}}}{\left(x - 5\right) \sqrt{- \frac{x}{\left(x - 5\right)^{2}} + 1}}$$
The third derivative
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2 / ___\ / ___\ / ___ \
/ 2*x \ | 1 2*\/ x | / 3*x \ | 1 2*\/ x | / 2*x \ | 1 8*\/ x 4 |
3*|-1 + ------| *|- ----- + -------| |-2 + ------|*|- ----- + -------| |-1 + ------|*|---- - --------- + --------------|
___ \ -5 + x/ | ___ -5 + x| \ -5 + x/ | ___ -5 + x| \ -5 + x/ | 3/2 2 ___ |
3 6*\/ x 3 3 \ \/ x / \ \/ x / \x (-5 + x) \/ x *(-5 + x)/
------ - --------- + --------------- + --------------- - ------------------------------------ - --------------------------------- + -------------------------------------------------
5/2 3 ___ 2 3/2 2 / x \ 3 / x \ 2
8*x (-5 + x) \/ x *(-5 + x) 4*x *(-5 + x) / x \ 4 2*|1 - ---------|*(-5 + x) 4*|1 - ---------|*(-5 + x)
8*|1 - ---------| *(-5 + x) | 2| | 2|
| 2| \ (-5 + x) / \ (-5 + x) /
\ (-5 + x) /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
_______________
/ x
/ 1 - --------- *(-5 + x)
/ 2
\/ (-5 + x)
$$\frac{- \frac{6 \sqrt{x}}{\left(x - 5\right)^{3}} + \frac{\left(\frac{2 x}{x - 5} - 1\right) \left(- \frac{8 \sqrt{x}}{\left(x - 5\right)^{2}} + \frac{4}{\sqrt{x} \left(x - 5\right)} + \frac{1}{x^{\frac{3}{2}}}\right)}{4 \left(x - 5\right)^{2} \left(- \frac{x}{\left(x - 5\right)^{2}} + 1\right)} - \frac{\left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right) \left(\frac{3 x}{x - 5} - 2\right)}{2 \left(x - 5\right)^{3} \left(- \frac{x}{\left(x - 5\right)^{2}} + 1\right)} - \frac{3 \left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right) \left(\frac{2 x}{x - 5} - 1\right)^{2}}{8 \left(x - 5\right)^{4} \left(- \frac{x}{\left(x - 5\right)^{2}} + 1\right)^{2}} + \frac{3}{\sqrt{x} \left(x - 5\right)^{2}} + \frac{3}{4 x^{\frac{3}{2}} \left(x - 5\right)} + \frac{3}{8 x^{\frac{5}{2}}}}{\left(x - 5\right) \sqrt{- \frac{x}{\left(x - 5\right)^{2}} + 1}}$$
3-я производная
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2 / ___\ / ___\ / ___ \
/ 2*x \ | 1 2*\/ x | / 3*x \ | 1 2*\/ x | / 2*x \ | 1 8*\/ x 4 |
3*|-1 + ------| *|- ----- + -------| |-2 + ------|*|- ----- + -------| |-1 + ------|*|---- - --------- + --------------|
___ \ -5 + x/ | ___ -5 + x| \ -5 + x/ | ___ -5 + x| \ -5 + x/ | 3/2 2 ___ |
3 6*\/ x 3 3 \ \/ x / \ \/ x / \x (-5 + x) \/ x *(-5 + x)/
------ - --------- + --------------- + --------------- - ------------------------------------ - --------------------------------- + -------------------------------------------------
5/2 3 ___ 2 3/2 2 / x \ 3 / x \ 2
8*x (-5 + x) \/ x *(-5 + x) 4*x *(-5 + x) / x \ 4 2*|1 - ---------|*(-5 + x) 4*|1 - ---------|*(-5 + x)
8*|1 - ---------| *(-5 + x) | 2| | 2|
| 2| \ (-5 + x) / \ (-5 + x) /
\ (-5 + x) /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
_______________
/ x
/ 1 - --------- *(-5 + x)
/ 2
\/ (-5 + x)
$$\frac{- \frac{6 \sqrt{x}}{\left(x - 5\right)^{3}} + \frac{\left(\frac{2 x}{x - 5} - 1\right) \left(- \frac{8 \sqrt{x}}{\left(x - 5\right)^{2}} + \frac{4}{\sqrt{x} \left(x - 5\right)} + \frac{1}{x^{\frac{3}{2}}}\right)}{4 \left(x - 5\right)^{2} \left(- \frac{x}{\left(x - 5\right)^{2}} + 1\right)} - \frac{\left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right) \left(\frac{3 x}{x - 5} - 2\right)}{2 \left(x - 5\right)^{3} \left(- \frac{x}{\left(x - 5\right)^{2}} + 1\right)} - \frac{3 \left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right) \left(\frac{2 x}{x - 5} - 1\right)^{2}}{8 \left(x - 5\right)^{4} \left(- \frac{x}{\left(x - 5\right)^{2}} + 1\right)^{2}} + \frac{3}{\sqrt{x} \left(x - 5\right)^{2}} + \frac{3}{4 x^{\frac{3}{2}} \left(x - 5\right)} + \frac{3}{8 x^{\frac{5}{2}}}}{\left(x - 5\right) \sqrt{- \frac{x}{\left(x - 5\right)^{2}} + 1}}$$
The graph