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

Given: Differentiate \( 2\cos^2 x \) with respect to \( \cos^2 x \). Let \( u = \cos^2 x \). The expression becomes \( 2u \). Differentiating \( 2u \) with respect to \( u \) yields \( \frac{d(2u)}{du} = 2 \). Therefore, \( \frac{d(2\cos^2 x)}{d(\cos^2 x)} = \mathbf{2} \).