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

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

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

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

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

2 sin (2 x)

Solution steps

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

Take the constant out:

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

= - 2 \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)

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

Simplify

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

= 2 sin (2 x)

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