What is the derivative of 2sin^3(5x) ?

The derivative of 2sin^3(5x) is 30sin^2(5x)cos(5x)

What is the first derivative of 2sin^3(5x) ?

The first derivative of 2sin^3(5x) is 30sin^2(5x)cos(5x)

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\frac{d}{d x} (2 sin^{3} (5 x))

30 sin^{2} (5 x) cos (5 x)

Solution steps

\frac{d}{d x} (2 sin^{3} (5 x))

Take the constant out:

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

= 2 \frac{d}{d x} (sin^{3} (5 x))

Apply the chain rule:

3 (sin (5 x))^{2} \frac{d}{d x} (sin (5 x))

= 3 (sin (5 x))^{2} \frac{d}{d x} (sin (5 x))

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

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

Simplify

= 30 sin^{2} (5 x) cos (5 x)

What is the derivative of 2sin^3(5x) ?
The derivative of 2sin^3(5x) is 30sin^2(5x)cos(5x)
What is the first derivative of 2sin^3(5x) ?
The first derivative of 2sin^3(5x) is 30sin^2(5x)cos(5x)