Step by step solution to "Find the derivative of this problem. h(x)=sin⁡2xcos⁡2x"

Susan Munoz

Answered question

2021-11-16

Find the derivative of this problem.

h (x) = \sin 2 x \cos 2 x

Thomas Conway

Beginner2021-11-17Added 10 answers

Product Rule of differentiation:
If

f (x)

and

g (x)

are two differentiable functions, then

{(f g)}^{'} (x) = f (x) \cdot g^{'} (x) + f^{'} (x) \cdot g (x)

The given function is

h (x) = \sin 2 x \cos 2 x

Differentiate the given dunction using the product rule as follows.

h^{'} (x) = \frac{d}{d x} (\sin 2 x \cos 2 x)

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

= \sin 2 x (- \sin 2 x) (2) + \cos (2 x) (\cos 2 x) (2)

= - 2 \sin^{2} 2 x + 2 \cos^{2} 2 x

= - 2 (1 - \cos^{2} 2 x) + 2 \cos^{2} 2 x

= - 2 (1 - \cos^{2} 2 x) + 2 \cos^{2} 2 x

= - 2 + 4 \cos^{2} 2 x

Therefore, the derivative of the given function is

h^{'} (x) = - 2 + 4 \cos^{2} 2 x

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