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

The derivative of sin^3(2x^2) is 12xsin^2(2x^2)cos(2x^2)

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

The first derivative of sin^3(2x^2) is 12xsin^2(2x^2)cos(2x^2)

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (sin (2 x^{2})) = cos (2 x^{2}) \cdot 4 x

= 3 (sin (2 x^{2}))^{2} cos (2 x^{2}) \cdot 4 x

Simplify

= 12 x sin^{2} (2 x^{2}) cos (2 x^{2})

What is the derivative of sin^3(2x^2) ?
The derivative of sin^3(2x^2) is 12xsin^2(2x^2)cos(2x^2)
What is the first derivative of sin^3(2x^2) ?
The first derivative of sin^3(2x^2) is 12xsin^2(2x^2)cos(2x^2)