What is the derivative of h(x)=5sin^3(3+x) ?

The derivative of h(x)=5sin^3(3+x) is 15sin^2(3+x)cos(3+x)

What is the first derivative of h(x)=5sin^3(3+x) ?

The first derivative of h(x)=5sin^3(3+x) is 15sin^2(3+x)cos(3+x)

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derivative of

h (x) = 5 sin^{3} (3 + x)

15 sin^{2} (3 + x) cos (3 + x)

Solution steps

\frac{d}{d x} (5 sin^{3} (3 + x))

Take the constant out:

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

= 5 \frac{d}{d x} (sin^{3} (3 + x))

Apply the chain rule:

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

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

\frac{d}{d x} (sin (3 + x)) = cos (3 + x)

= 5 \cdot 3 (sin (3 + x))^{2} cos (3 + x)

Simplify

= 15 sin^{2} (3 + x) cos (3 + x)

What is the derivative of h(x)=5sin^3(3+x) ?
The derivative of h(x)=5sin^3(3+x) is 15sin^2(3+x)cos(3+x)
What is the first derivative of h(x)=5sin^3(3+x) ?
The first derivative of h(x)=5sin^3(3+x) is 15sin^2(3+x)cos(3+x)