What is the derivative of 1/3 sin^3(x) ?

The derivative of 1/3 sin^3(x) is sin^2(x)cos(x)

What is the first derivative of 1/3 sin^3(x) ?

The first derivative of 1/3 sin^3(x) is sin^2(x)cos(x)

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\frac{d}{d x} (\frac{1}{3} sin^{3} (x))

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

Solution steps

\frac{d}{d x} (\frac{1}{3} sin^{3} (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{3} \frac{d}{d x} (sin^{3} (x))

Apply the chain rule:

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

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

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

= \frac{1}{3} \cdot 3 (sin (x))^{2} cos (x)

Simplify

\frac{1}{3} \cdot 3 sin^{2} (x) cos (x) : sin^{2} (x) cos (x)

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

What is the derivative of 1/3 sin^3(x) ?
The derivative of 1/3 sin^3(x) is sin^2(x)cos(x)
What is the first derivative of 1/3 sin^3(x) ?
The first derivative of 1/3 sin^3(x) is sin^2(x)cos(x)