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

The derivative of 2cos^2(x^2+2) is -8xcos(x^2+2)sin(x^2+2)

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

The first derivative of 2cos^2(x^2+2) is -8xcos(x^2+2)sin(x^2+2)

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

- 8 x cos (x^{2} + 2) sin (x^{2} + 2)

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

= - 8 x cos (x^{2} + 2) sin (x^{2} + 2)

What is the derivative of 2cos^2(x^2+2) ?
The derivative of 2cos^2(x^2+2) is -8xcos(x^2+2)sin(x^2+2)
What is the first derivative of 2cos^2(x^2+2) ?
The first derivative of 2cos^2(x^2+2) is -8xcos(x^2+2)sin(x^2+2)