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