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- Derivative of:
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Derivative of z
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Derivative of x^2*atanh(x)*acoth(x)
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Derivative of -cos(x)
- Derivative of -4
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Identical expressions
- log(three)*arcsin(sqrt(x)/(x- five))
- logarithm of (3) multiply by arc sinus of ( square root of (x) divide by (x minus 5))
- logarithm of (three) multiply by arc sinus of ( square root of (x) divide by (x minus five))
- log(3)*arcsin(√(x)/(x-5))
- log(3)arcsin(sqrt(x)/(x-5))
- log3arcsinsqrtx/x-5
- log(3)*arcsin(sqrt(x) divide by (x-5))
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Similar expressions
- log(3)*arcsin(sqrt(x)/(x+5))
- log3(arcsin(sqrt(x)/(x-5)))
Derivative of log(3)*arcsin(sqrt(x)/(x-5))
The solution
You have entered
[src]
/ ___\
|\/ x |
log(3)*asin|-----|
\x - 5/
$$\log{\left(3 \right)} \operatorname{asin}{\left(\frac{\sqrt{x}}{x - 5} \right)}$$
The first derivative
[src]
/ ___ \
| 1 \/ x |
|--------------- - --------|*log(3)
| ___ 2|
\2*\/ x *(x - 5) (x - 5) /
-----------------------------------
______________
/ x
/ 1 - --------
/ 2
\/ (x - 5)
$$\frac{\left(- \frac{\sqrt{x}}{\left(x - 5\right)^{2}} + \frac{1}{2 \sqrt{x} \left(x - 5\right)}\right) \log{\left(3 \right)}}{\sqrt{- \frac{x}{\left(x - 5\right)^{2}} + 1}}$$
The second derivative
[src]
/ / ___\\
| / 2*x \ | 1 2*\/ x ||
| |-1 + ------|*|- ----- + -------||
| ___ \ -5 + x/ | ___ -5 + x||
| 1 1 2*\/ x \ \/ x /|
-|------ + -------------- - --------- + ---------------------------------|*log(3)
| 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)
$$- \frac{\left(- \frac{2 \sqrt{x}}{\left(x - 5\right)^{2}} + \frac{\left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right) \left(\frac{2 x}{x - 5} - 1\right)}{4 \left(x - 5\right)^{2} \left(\frac{x}{\left(x - 5\right)^{2}} - 1\right)} + \frac{1}{\sqrt{x} \left(x - 5\right)} + \frac{1}{4 x^{\frac{3}{2}}}\right) \log{\left(3 \right)}}{\left(x - 5\right) \sqrt{- \frac{x}{\left(x - 5\right)^{2}} + 1}}$$
The third derivative
[src]
/ / ___\ 2 / ___\ / ___ \\
| / 3*x \ | 1 2*\/ x | / 2*x \ | 1 2*\/ x | / 2*x \ | 1 8*\/ x 4 ||
| |-2 + ------|*|- ----- + -------| 3*|-1 + ------| *|- ----- + -------| |-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)/|
|------ - --------- + --------------- + --------------- + --------------------------------- - ------------------------------------ - -------------------------------------------------|*log(3)
| 5/2 3 ___ 2 3/2 / x \ 3 2 / x \ 2 |
|8*x (-5 + x) \/ x *(-5 + x) 4*x *(-5 + x) 2*|-1 + ---------|*(-5 + x) / x \ 4 4*|-1 + ---------|*(-5 + x) |
| | 2| 8*|-1 + ---------| *(-5 + x) | 2| |
| \ (-5 + x) / | 2| \ (-5 + x) / |
\ \ (-5 + x) / /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
_______________
/ x
/ 1 - --------- *(-5 + x)
/ 2
\/ (-5 + x)
$$\frac{\left(- \frac{6 \sqrt{x}}{\left(x - 5\right)^{3}} - \frac{\left(\frac{2 x}{x - 5} - 1\right) \left(- \frac{8 \sqrt{x}}{\left(x - 5\right)^{2}} + \frac{4}{\sqrt{x} \left(x - 5\right)} + \frac{1}{x^{\frac{3}{2}}}\right)}{4 \left(x - 5\right)^{2} \left(\frac{x}{\left(x - 5\right)^{2}} - 1\right)} + \frac{\left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right) \left(\frac{3 x}{x - 5} - 2\right)}{2 \left(x - 5\right)^{3} \left(\frac{x}{\left(x - 5\right)^{2}} - 1\right)} - \frac{3 \left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right) \left(\frac{2 x}{x - 5} - 1\right)^{2}}{8 \left(x - 5\right)^{4} \left(\frac{x}{\left(x - 5\right)^{2}} - 1\right)^{2}} + \frac{3}{\sqrt{x} \left(x - 5\right)^{2}} + \frac{3}{4 x^{\frac{3}{2}} \left(x - 5\right)} + \frac{3}{8 x^{\frac{5}{2}}}\right) \log{\left(3 \right)}}{\left(x - 5\right) \sqrt{- \frac{x}{\left(x - 5\right)^{2}} + 1}}$$
The graph