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Derivative of:
Derivative of 4x^3
Derivative of x^4-2x^2+2
Derivative of tg^2×(2x)
Derivative of arcsin(x)^sqrt(1-x^2)
Identical expressions
arcsin(x)^sqrt(one -x^ two)
arc sinus of (x) to the power of square root of (1 minus x squared )
arc sinus of (x) to the power of square root of (one minus x to the power of two)
arcsin(x)^√(1-x^2)
arcsin(x)sqrt(1-x2)
arcsinxsqrt1-x2
arcsin(x)^sqrt(1-x²)
arcsin(x) to the power of sqrt(1-x to the power of 2)
arcsinx^sqrt1-x^2
Similar expressions
arcsin(x)^sqrt(1+x^2)
arcsinx^sqrt(1-x^2)

The derivative of the function/ arcsin(x)^sqrt(1-x^2)

Derivative of arcsin(x)^sqrt(1-x^2)

The solution

You have entered [src]

            ________
           /      2 
         \/  1 - x  
(asin(x))

$$\operatorname{asin}^{\sqrt{- x^{2} + 1}}{\left(x \right)}$$

  /            ________\
  |           /      2 |
d |         \/  1 - x  |
--\(asin(x))           /
dx

$$\frac{d}{d x} \operatorname{asin}^{\sqrt{- x^{2} + 1}}{\left(x \right)}$$

Transform

Detail solution

Don't know the steps in finding this derivative.

But the derivative is

$\left(1 - x^{2}\right)^{\frac{\sqrt{1 - x^{2}}}{2}} \left(\log{\left(\sqrt{1 - x^{2}} \right)} + 1\right)$
Now simplify:

$\frac{\left(1 - x^{2}\right)^{\frac{\sqrt{1 - x^{2}}}{2}} \left(\log{\left(1 - x^{2} \right)} + 2\right)}{2}$

The answer is:

$\frac{\left(1 - x^{2}\right)^{\frac{\sqrt{1 - x^{2}}}{2}} \left(\log{\left(1 - x^{2} \right)} + 2\right)}{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

            ________                           
           /      2                            
         \/  1 - x   /   1      x*log(asin(x))\
(asin(x))           *|------- - --------------|
                     |asin(x)       ________  |
                     |             /      2   |
                     \           \/  1 - x    /

$$\left(- \frac{x \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\sqrt{- x^{2} + 1}} + \frac{1}{\operatorname{asin}{\left(x \right)}}\right) \operatorname{asin}^{\sqrt{- x^{2} + 1}}{\left(x \right)}$$

Simplify

The second derivative [src]

            ________                                                                                                            
           /      2  /                            2                                                              2             \
         \/  1 - x   |/     1      x*log(asin(x))\             1             log(asin(x))           x           x *log(asin(x))|
(asin(x))           *||- ------- + --------------|  - -------------------- - ------------ + ----------------- - ---------------|
                     ||  asin(x)       ________  |       ________               ________    /      2\                     3/2  |
                     ||               /      2   |      /      2      2        /      2     \-1 + x /*asin(x)     /     2\     |
                     \\             \/  1 - x    /    \/  1 - x  *asin (x)   \/  1 - x                            \1 - x /     /

$$\left(\left(\frac{x \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\sqrt{- x^{2} + 1}} - \frac{1}{\operatorname{asin}{\left(x \right)}}\right)^{2} - \frac{x^{2} \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\sqrt{- x^{2} + 1}} + \frac{x}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}} - \frac{1}{\sqrt{- x^{2} + 1} \operatorname{asin}^{2}{\left(x \right)}}\right) \operatorname{asin}^{\sqrt{- x^{2} + 1}}{\left(x \right)}$$

Simplify

The third derivative [src]

            ________                                                                                                                                                                                                                                                    
           /      2  /                              3                                                                           /                                       2                                 \                                2             3             \
         \/  1 - x   |  /     1      x*log(asin(x))\            2                    2             /     1      x*log(asin(x))\ |         1             log(asin(x))   x *log(asin(x))           x        |   3*x*log(asin(x))          3*x           3*x *log(asin(x))|
(asin(x))           *|- |- ------- + --------------|  - ------------------ + ----------------- + 3*|- ------- + --------------|*|-------------------- + ------------ + --------------- - -----------------| - ---------------- - ------------------ - -----------------|
                     |  |  asin(x)       ________  |    /      2\     3      /      2\             |  asin(x)       ________  | |   ________               ________              3/2     /      2\        |             3/2               2                      5/2   |
                     |  |               /      2   |    \-1 + x /*asin (x)   \-1 + x /*asin(x)     |               /      2   | |  /      2      2        /      2       /     2\        \-1 + x /*asin(x)|     /     2\         /      2\               /     2\      |
                     \  \             \/  1 - x    /                                               \             \/  1 - x    / \\/  1 - x  *asin (x)   \/  1 - x        \1 - x /                         /     \1 - x /         \-1 + x / *asin(x)      \1 - x /      /

$$\left(- \left(\frac{x \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\sqrt{- x^{2} + 1}} - \frac{1}{\operatorname{asin}{\left(x \right)}}\right)^{3} + 3 \left(\frac{x \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\sqrt{- x^{2} + 1}} - \frac{1}{\operatorname{asin}{\left(x \right)}}\right) \left(\frac{x^{2} \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\sqrt{- x^{2} + 1}} - \frac{x}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}} + \frac{1}{\sqrt{- x^{2} + 1} \operatorname{asin}^{2}{\left(x \right)}}\right) - \frac{3 x^{3} \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} - \frac{3 x^{2}}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left(x \right)}} - \frac{3 x \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{2}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}} - \frac{2}{\left(x^{2} - 1\right) \operatorname{asin}^{3}{\left(x \right)}}\right) \operatorname{asin}^{\sqrt{- x^{2} + 1}}{\left(x \right)}$$

Simplify

The graph

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Identical expressions

Similar expressions

Derivative of arcsin(x)^sqrt(1-x^2)

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Piecewise:

The solution