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 of

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

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)

y = 8 x^{3} - 5 x^{2} - \frac{x}{12}

(x^{5} + 5)^{\frac{4}{3}} tan (2 x)

arctan (\frac{x}{1 - x})

\frac{d}{d x} (x^{0.45})

\frac{\partial}{\partial x} (ln (x^{4} + y^{4}))

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)