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- Derivative of:
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Derivative of 2*x^5
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Derivative of y=(x^3-3)(x^2+4x+1)
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Derivative of y=12x+√x
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Derivative of x*e^x+11
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Identical expressions
- log3(arcsin(sqrt(x)/(x- five)))
- logarithm of 3(arc sinus of ( square root of (x) divide by (x minus 5)))
- logarithm of 3(arc sinus of ( square root of (x) divide by (x minus five)))
- log3(arcsin(√(x)/(x-5)))
- log3arcsinsqrtx/x-5
- log3(arcsin(sqrt(x) divide by (x-5)))
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Similar expressions
- log3(arcsin(sqrt(x)/(x+5)))
Derivative of log3(arcsin(sqrt(x)/(x-5)))
The solution
You have entered
[src]
/ / ___\\
| |\/ x ||
log|asin|-----||
\ \x - 5//
----------------
log(3)
$$\frac{\log{\left(\operatorname{asin}{\left(\frac{\sqrt{x}}{x - 5} \right)} \right)}}{\log{\left(3 \right)}}$$
The first derivative
[src]
___
1 \/ x
--------------- - --------
___ 2
2*\/ x *(x - 5) (x - 5)
--------------------------------------
______________ / ___\
/ x |\/ x |
/ 1 - -------- *asin|-----|*log(3)
/ 2 \x - 5/
\/ (x - 5)
$$\frac{- \frac{\sqrt{x}}{\left(x - 5\right)^{2}} + \frac{1}{2 \sqrt{x} \left(x - 5\right)}}{\sqrt{- \frac{x}{\left(x - 5\right)^{2}} + 1} \log{\left(3 \right)} \operatorname{asin}{\left(\frac{\sqrt{x}}{x - 5} \right)}}$$
The second derivative
[src]
2
___ / ___\ / ___\
1 8*\/ x 4 / 2*x \ | 1 2*\/ x | | 1 2*\/ x |
---- - --------- + -------------- |-1 + ------|*|- ----- + -------| |- ----- + -------|
3/2 2 ___ \ -5 + x/ | ___ -5 + x| | ___ -5 + x|
x (-5 + x) \/ x *(-5 + x) \ \/ x / \ \/ x /
- --------------------------------- + --------------------------------- + --------------------------------------
_______________ 3/2 / ___ \
/ x / x \ 2 / x \ |\/ x |
/ 1 - --------- |1 - ---------| *(-5 + x) |-1 + ---------|*(-5 + x)*asin|------|
/ 2 | 2| | 2| \-5 + x/
\/ (-5 + x) \ (-5 + x) / \ (-5 + x) /
----------------------------------------------------------------------------------------------------------------
/ ___ \
|\/ x |
4*(-5 + x)*asin|------|*log(3)
\-5 + x/
$$\frac{- \frac{- \frac{8 \sqrt{x}}{\left(x - 5\right)^{2}} + \frac{4}{\sqrt{x} \left(x - 5\right)} + \frac{1}{x^{\frac{3}{2}}}}{\sqrt{- \frac{x}{\left(x - 5\right)^{2}} + 1}} + \frac{\left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right)^{2}}{\left(x - 5\right) \left(\frac{x}{\left(x - 5\right)^{2}} - 1\right) \operatorname{asin}{\left(\frac{\sqrt{x}}{x - 5} \right)}} + \frac{\left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right) \left(\frac{2 x}{x - 5} - 1\right)}{\left(x - 5\right)^{2} \left(- \frac{x}{\left(x - 5\right)^{2}} + 1\right)^{\frac{3}{2}}}}{4 \left(x - 5\right) \log{\left(3 \right)} \operatorname{asin}{\left(\frac{\sqrt{x}}{x - 5} \right)}}$$
The third derivative
[src]
3 2
/ ___ \ / ___\ 2 / ___\ / ___\ / ___ \ / ___\ / ___ \ / ___\
| 1 16*\/ x 2 8 | / 3*x \ | 1 2*\/ x | / 2*x \ | 1 2*\/ x | | 1 2*\/ x | / 2*x \ | 1 8*\/ x 4 | | 1 2*\/ x | | 1 8*\/ x 4 | | 1 2*\/ x | / 2*x \
3*|---- - --------- + ------------- + ---------------| 4*|-2 + ------|*|- ----- + -------| 3*|-1 + ------| *|- ----- + -------| 2*|- ----- + -------| 2*|-1 + ------|*|---- - --------- + --------------| 3*|- ----- + -------|*|---- - --------- + --------------| 3*|- ----- + -------| *|-1 + ------|
| 5/2 3 3/2 ___ 2| \ -5 + x/ | ___ -5 + x| \ -5 + x/ | ___ -5 + x| | ___ -5 + x| \ -5 + x/ | 3/2 2 ___ | | ___ -5 + x| | 3/2 2 ___ | | ___ -5 + x| \ -5 + x/
\x (-5 + x) x *(-5 + x) \/ x *(-5 + x) / \ \/ x / \ \/ x / \ \/ x / \x (-5 + x) \/ x *(-5 + x)/ \ \/ x / \x (-5 + x) \/ x *(-5 + x)/ \ \/ x /
------------------------------------------------------ - ----------------------------------- - ------------------------------------ - ------------------------------------------ + --------------------------------------------------- + --------------------------------------------------------- + ----------------------------------------
_______________ 3/2 5/2 3/2 / ___ \ 3/2 / ___ \ 2 / ___ \
/ x / x \ 3 / x \ 4 / x \ 2 2|\/ x | / x \ 2 / x \ |\/ x | / x \ 3 |\/ x |
/ 1 - --------- |1 - ---------| *(-5 + x) |1 - ---------| *(-5 + x) |1 - ---------| *(-5 + x) *asin |------| |1 - ---------| *(-5 + x) |-1 + ---------|*(-5 + x)*asin|------| |-1 + ---------| *(-5 + x) *asin|------|
/ 2 | 2| | 2| | 2| \-5 + x/ | 2| | 2| \-5 + x/ | 2| \-5 + x/
\/ (-5 + x) \ (-5 + x) / \ (-5 + x) / \ (-5 + x) / \ (-5 + x) / \ (-5 + x) / \ (-5 + x) /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ ___ \
|\/ x |
8*(-5 + x)*asin|------|*log(3)
\-5 + x/
$$\frac{\frac{3 \left(- \frac{16 \sqrt{x}}{\left(x - 5\right)^{3}} + \frac{8}{\sqrt{x} \left(x - 5\right)^{2}} + \frac{2}{x^{\frac{3}{2}} \left(x - 5\right)} + \frac{1}{x^{\frac{5}{2}}}\right)}{\sqrt{- \frac{x}{\left(x - 5\right)^{2}} + 1}} + \frac{3 \left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right) \left(- \frac{8 \sqrt{x}}{\left(x - 5\right)^{2}} + \frac{4}{\sqrt{x} \left(x - 5\right)} + \frac{1}{x^{\frac{3}{2}}}\right)}{\left(x - 5\right) \left(\frac{x}{\left(x - 5\right)^{2}} - 1\right) \operatorname{asin}{\left(\frac{\sqrt{x}}{x - 5} \right)}} - \frac{2 \left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right)^{3}}{\left(x - 5\right)^{2} \left(- \frac{x}{\left(x - 5\right)^{2}} + 1\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(\frac{\sqrt{x}}{x - 5} \right)}} + \frac{2 \left(\frac{2 x}{x - 5} - 1\right) \left(- \frac{8 \sqrt{x}}{\left(x - 5\right)^{2}} + \frac{4}{\sqrt{x} \left(x - 5\right)} + \frac{1}{x^{\frac{3}{2}}}\right)}{\left(x - 5\right)^{2} \left(- \frac{x}{\left(x - 5\right)^{2}} + 1\right)^{\frac{3}{2}}} + \frac{3 \left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right)^{2} \left(\frac{2 x}{x - 5} - 1\right)}{\left(x - 5\right)^{3} \left(\frac{x}{\left(x - 5\right)^{2}} - 1\right)^{2} \operatorname{asin}{\left(\frac{\sqrt{x}}{x - 5} \right)}} - \frac{4 \left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right) \left(\frac{3 x}{x - 5} - 2\right)}{\left(x - 5\right)^{3} \left(- \frac{x}{\left(x - 5\right)^{2}} + 1\right)^{\frac{3}{2}}} - \frac{3 \left(\frac{2 \sqrt{x}}{x - 5} - \frac{1}{\sqrt{x}}\right) \left(\frac{2 x}{x - 5} - 1\right)^{2}}{\left(x - 5\right)^{4} \left(- \frac{x}{\left(x - 5\right)^{2}} + 1\right)^{\frac{5}{2}}}}{8 \left(x - 5\right) \log{\left(3 \right)} \operatorname{asin}{\left(\frac{\sqrt{x}}{x - 5} \right)}}$$
The graph