What is the derivative of sin^3(4x) ?

The derivative of sin^3(4x) is 12sin^2(4x)cos(4x)

What is the first derivative of sin^3(4x) ?

The first derivative of sin^3(4x) is 12sin^2(4x)cos(4x)

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

12 sin^{2} (4 x) cos (4 x)

Solution steps

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

Apply the chain rule:

3 (sin (4 x))^{2} \frac{d}{d x} (sin (4 x))

= 3 (sin (4 x))^{2} \frac{d}{d x} (sin (4 x))

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

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

Simplify

= 12 sin^{2} (4 x) cos (4 x)

What is the derivative of sin^3(4x) ?
The derivative of sin^3(4x) is 12sin^2(4x)cos(4x)
What is the first derivative of sin^3(4x) ?
The first derivative of sin^3(4x) is 12sin^2(4x)cos(4x)