Question

Differentiate $2\cos^2 x$ w.r.t. $\cos^2 x$.

Hint:

To differentiate $\cos^2 x$, remember to use the chain rule as $\frac{d}{dx}[\cos^2 x] = 2\cos x \cdot \frac{d}{dx}[\cos x]$.

Answer 1

Using the chain rule, we differentiate $2\cos^2 x$: \[ \frac{d}{dx}(2 \cos^2 x) = 2 \times 2\cos x \times (-\sin x) = -4 \cos x \sin x \] Thus, the derivative of $2 \cos^2 x$ with respect to $x$ is $-4 \cos x \sin x$.