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

The derivative of 3sin^2(2x) is 12sin(2x)cos(2x)

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

The first derivative of 3sin^2(2x) is 12sin(2x)cos(2x)

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

12 sin (2 x) cos (2 x)

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= 3 \cdot 2 sin (2 x) cos (2 x) \cdot 2

Simplify

= 12 sin (2 x) cos (2 x)

What is the derivative of 3sin^2(2x) ?
The derivative of 3sin^2(2x) is 12sin(2x)cos(2x)
What is the first derivative of 3sin^2(2x) ?
The first derivative of 3sin^2(2x) is 12sin(2x)cos(2x)