What is the derivative of sin^2(2bx) ?

The derivative of sin^2(2bx) is 4bsin(2bx)cos(2bx)

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

The first derivative of sin^2(2bx) is 4bsin(2bx)cos(2bx)

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

4 b sin (2 b x) cos (2 b x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

= 4 b sin (2 b x) cos (2 b x)

What is the derivative of sin^2(2bx) ?
The derivative of sin^2(2bx) is 4bsin(2bx)cos(2bx)
What is the first derivative of sin^2(2bx) ?
The first derivative of sin^2(2bx) is 4bsin(2bx)cos(2bx)