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

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

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

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

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derivative

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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