What is the derivative of sin^{-3}(x) ?

The derivative of sin^{-3}(x) is -(3cos(x))/(sin^4(x))

What is the first derivative of sin^{-3}(x) ?

The first derivative of sin^{-3}(x) is -(3cos(x))/(sin^4(x))

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\frac{d}{d x} (sin^{- 3} (x))

- \frac{3 cos ( x )}{sin ^{4} ( x )}

Solution steps

\frac{d}{d x} (sin^{- 3} (x))

Apply the chain rule:

- \frac{3}{( sin ( x ) ) ^{4}} \frac{d}{d x} (sin (x))

= - \frac{3}{( sin ( x ) ) ^{4}} \frac{d}{d x} (sin (x))

\frac{d}{d x} (sin (x)) = cos (x)

= - \frac{3}{( sin ( x ) ) ^{4}} cos (x)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{3 cos ( x )}{sin ^{4} ( x )}

What is the derivative of sin^{-3}(x) ?
The derivative of sin^{-3}(x) is -(3cos(x))/(sin^4(x))
What is the first derivative of sin^{-3}(x) ?
The first derivative of sin^{-3}(x) is -(3cos(x))/(sin^4(x))