What is the derivative of sin^3(x^2) ?

The derivative of sin^3(x^2) is 6xsin^2(x^2)cos(x^2)

What is the first derivative of sin^3(x^2) ?

The first derivative of sin^3(x^2) is 6xsin^2(x^2)cos(x^2)

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derivative of

sin^{3} (x^{2})

6 x sin^{2} (x^{2}) cos (x^{2})

Solution steps

\frac{d}{d x} (sin^{3} (x^{2}))

Apply the chain rule:

3 (sin (x^{2}))^{2} \frac{d}{d x} (sin (x^{2}))

= 3 (sin (x^{2}))^{2} \frac{d}{d x} (sin (x^{2}))

\frac{d}{d x} (sin (x^{2})) = cos (x^{2}) \cdot 2 x

= 3 (sin (x^{2}))^{2} cos (x^{2}) \cdot 2 x

Simplify

= 6 x sin^{2} (x^{2}) cos (x^{2})

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

x \to 49 lim (x^{\frac{3}{2}})

\int \frac{x ^{4}}{4} - \frac{x ^{3}}{3} + 5 x d x

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

\frac{4 s}{4 s ^{2} + 1}

What is the derivative of sin^3(x^2) ?
The derivative of sin^3(x^2) is 6xsin^2(x^2)cos(x^2)
What is the first derivative of sin^3(x^2) ?
The first derivative of sin^3(x^2) is 6xsin^2(x^2)cos(x^2)