Mister Exam
Other calculators
- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Derivative of:
-
Derivative of -6/x
-
Derivative of -2*y
-
Derivative of ln(x)+x
-
Derivative of cosx-3x
-
Identical expressions
- (arcsin(x))^(sqrt(x))
- (arc sinus of (x)) to the power of ( square root of (x))
- (arcsin(x))^(√(x))
- (arcsin(x))(sqrt(x))
- arcsinxsqrtx
- arcsinx^sqrtx
-
Similar expressions
- (arcsinx)^(sqrt(x))
Derivative of (arcsin(x))^(sqrt(x))
The solution
You have entered
[src]
___
\/ x
(asin(x))
$$\operatorname{asin}^{\sqrt{x}}{\left(x \right)}$$
asin(x)^(sqrt(x))
Detail solution
-
Don't know the steps in finding this derivative.
But the derivative is
-
Now simplify:
The answer is:
The first derivative
[src]
___ / ___ \
\/ x |log(asin(x)) \/ x |
(asin(x)) *|------------ + -------------------|
| ___ ________ |
| 2*\/ x / 2 |
\ \/ 1 - x *asin(x)/
$$\left(\frac{\sqrt{x}}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \operatorname{asin}^{\sqrt{x}}{\left(x \right)}$$
The second derivative
[src]
/ 2 \
|/ ___ \ |
||log(asin(x)) 2*\/ x | |
||------------ + -------------------| |
|| ___ ________ | |
___ || \/ x / 2 | ___ 3/2 |
\/ x |\ \/ 1 - x *asin(x)/ log(asin(x)) \/ x 1 x |
(asin(x)) *|------------------------------------- - ------------ + ------------------ + ------------------------- + -------------------|
| 4 3/2 / 2\ 2 ________ 3/2 |
| 4*x \-1 + x /*asin (x) ___ / 2 / 2\ |
\ \/ x *\/ 1 - x *asin(x) \1 - x / *asin(x)/
$$\left(\frac{x^{\frac{3}{2}}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \frac{\sqrt{x}}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left(x \right)}} + \frac{\left(\frac{2 \sqrt{x}}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\sqrt{x}}\right)^{2}}{4} + \frac{1}{\sqrt{x} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} - \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{4 x^{\frac{3}{2}}}\right) \operatorname{asin}^{\sqrt{x}}{\left(x \right)}$$
The third derivative
[src]
/ 3 \
|/ ___ \ / ___ \ / ___ 3/2 \ |
||log(asin(x)) 2*\/ x | |log(asin(x)) 2*\/ x | | log(asin(x)) 4*\/ x 4 4*x | |
||------------ + -------------------| 3*|------------ + -------------------|*|- ------------ + ------------------ + ------------------------- + -------------------| |
|| ___ ________ | | ___ ________ | | 3/2 / 2\ 2 ________ 3/2 | |
___ || \/ x / 2 | | \/ x / 2 | | x \-1 + x /*asin (x) ___ / 2 / 2\ | 3/2 ___ 5/2 ___ |
\/ x |\ \/ 1 - x *asin(x)/ 3*log(asin(x)) \ \/ 1 - x *asin(x)/ \ \/ x *\/ 1 - x *asin(x) \1 - x / *asin(x)/ 3*x 2*\/ x 3*x 3 3 5*\/ x |
(asin(x)) *|------------------------------------- + -------------- + ------------------------------------------------------------------------------------------------------------------------------ - ------------------- + -------------------- + ------------------- - -------------------------- + -------------------------- + ---------------------|
| 8 5/2 8 2 3/2 5/2 ________ ___ / 2\ 2 3/2 |
| 8*x / 2\ 2 / 2\ 3 / 2\ 3/2 / 2 2*\/ x *\-1 + x /*asin (x) / 2\ |
\ \-1 + x / *asin (x) \1 - x / *asin (x) \1 - x / *asin(x) 4*x *\/ 1 - x *asin(x) 2*\1 - x / *asin(x)/
$$\left(\frac{3 x^{\frac{5}{2}}}{\left(1 - x^{2}\right)^{\frac{5}{2}} \operatorname{asin}{\left(x \right)}} - \frac{3 x^{\frac{3}{2}}}{\left(x^{2} - 1\right)^{2} \operatorname{asin}^{2}{\left(x \right)}} + \frac{5 \sqrt{x}}{2 \left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \frac{2 \sqrt{x}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{3}{\left(x \right)}} + \frac{\left(\frac{2 \sqrt{x}}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\sqrt{x}}\right)^{3}}{8} + \frac{3 \left(\frac{2 \sqrt{x}}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\sqrt{x}}\right) \left(\frac{4 x^{\frac{3}{2}}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \frac{4 \sqrt{x}}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left(x \right)}} + \frac{4}{\sqrt{x} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} - \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x^{\frac{3}{2}}}\right)}{8} + \frac{3}{2 \sqrt{x} \left(x^{2} - 1\right) \operatorname{asin}^{2}{\left(x \right)}} - \frac{3}{4 x^{\frac{3}{2}} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{3 \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{8 x^{\frac{5}{2}}}\right) \operatorname{asin}^{\sqrt{x}}{\left(x \right)}$$