What is the derivative of (2cos(x)^2) ?

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

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

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

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

- 4 sin (2 x)

Solution steps

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

Simplify

(2 cos (x))^{2} : 4 cos^{2} (x)

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - 4 sin (2 x)

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