What is (\partial)/(\partial x)(cos^2(2x)) ?

The answer to (\partial)/(\partial x)(cos^2(2x)) is -2sin(4x)

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(\partial)/(\partial x)(cos^2(2x))

\frac{\partial}{\partial x} (cos^{2} (2 x))

- 2 sin (4 x)

Solution steps

\frac{\partial}{\partial x} (cos^{2} (2 x))

Apply the chain rule:

2 cos (2 x) \frac{\partial}{\partial x} (cos (2 x))

= 2 cos (2 x) \frac{\partial}{\partial x} (cos (2 x))

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

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

Simplify

2 cos (2 x) (- sin (2 x) \cdot 2) : - 2 sin (4 x)

= - 2 sin (4 x)

x \to 0 lim (- cos (\frac{1}{x}))

f (x) = 4 x^{2} + 2 x, at x = 2

\frac{\partial}{\partial x} (sech^{2} (x - t))

\int x^{3} cos (x^{4} + 2) d x

\int_{0}^{3} \frac{3 t}{( t - 4 ) ^{2}} d t

What is (\partial)/(\partial x)(cos^2(2x)) ?
The answer to (\partial)/(\partial x)(cos^2(2x)) is -2sin(4x)