What is the derivative of (arcsin(1-x^2)^4) ?

The derivative of (arcsin(1-x^2)^4) is -(8arcsin^3(1-x^2))/(sqrt(-x^2+2))

What is the first derivative of (arcsin(1-x^2)^4) ?

The first derivative of (arcsin(1-x^2)^4) is -(8arcsin^3(1-x^2))/(sqrt(-x^2+2))

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\frac{d}{d x} ((arcsin (1 - x^{2}))^{4})

- \frac{8 arcsin ^{3} ( 1 - x ^{2} )}{- x ^{2} + 2}

Solution steps

\frac{d}{d x} ((arcsin (1 - x^{2}))^{4})

Apply the chain rule:

4 (arcsin (1 - x^{2}))^{3} \frac{d}{d x} (arcsin (1 - x^{2}))

= 4 (arcsin (1 - x^{2}))^{3} \frac{d}{d x} (arcsin (1 - x^{2}))

\frac{d}{d x} (arcsin (1 - x^{2})) = - \frac{2 x}{x ^{2} - x ^{2} + 2}

= 4 (arcsin (1 - x^{2}))^{3} (- \frac{2 x}{x ^{2} - x ^{2} + 2})

Simplify

4 arcsin^{3} (1 - x^{2}) (- \frac{2 x}{x ^{2} - x ^{2} + 2}) : - \frac{8 arcsin ^{3} ( 1 - x ^{2} )}{- x ^{2} + 2}

= - \frac{8 arcsin ^{3} ( 1 - x ^{2} )}{- x ^{2} + 2}

\int_{1}^{2} 2 x^{4} ln (x) d x

\int y x e^{x y} d y

e^{- 2 x}, 0

\frac{d}{d x} (x + x^{2} - 1)

\int \frac{s \cdot ln ( s )}{( 1 - s ^{2} ) ^{\frac{1}{2}}} d s

What is the derivative of (arcsin(1-x^2)^4) ?
The derivative of (arcsin(1-x^2)^4) is -(8arcsin^3(1-x^2))/(sqrt(-x^2+2))
What is the first derivative of (arcsin(1-x^2)^4) ?
The first derivative of (arcsin(1-x^2)^4) is -(8arcsin^3(1-x^2))/(sqrt(-x^2+2))