What is the derivative of sqrt(4cos(2x)) ?

The derivative of sqrt(4cos(2x)) is -2sin(2x)sqrt(sec(2x))

What is the first derivative of sqrt(4cos(2x)) ?

The first derivative of sqrt(4cos(2x)) is -2sin(2x)sqrt(sec(2x))

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\frac{d}{d x} (4 cos (2 x))

- 2 sin (2 x) sec (2 x)

Solution steps

\frac{d}{d x} (4 cos (2 x))

Apply the chain rule:

\frac{1}{2 4 cos ( 2 x )} \frac{d}{d x} (4 cos (2 x))

= \frac{1}{2 4 cos ( 2 x )} \frac{d}{d x} (4 cos (2 x))

\frac{d}{d x} (4 cos (2 x)) = - 8 sin (2 x)

= \frac{1}{2 4 cos ( 2 x )} (- 8 sin (2 x))

Simplify

\frac{1}{2 4 cos ( 2 x )} (- 8 sin (2 x)) : - 2 sin (2 x) sec (2 x)

= - 2 sin (2 x) sec (2 x)

What is the derivative of sqrt(4cos(2x)) ?
The derivative of sqrt(4cos(2x)) is -2sin(2x)sqrt(sec(2x))
What is the first derivative of sqrt(4cos(2x)) ?
The first derivative of sqrt(4cos(2x)) is -2sin(2x)sqrt(sec(2x))