JAMB 2004 · UME · Q37

If $y = 3\cos\frac x3$ , find $\frac{dy}{dx}$ when $x = \frac{3\pi}{2}$ .

Worked solution (try it first)

Chain rule: $\cos\frac x3$ differentiates to $-\frac13\sin\frac x3$ , so $\frac{dy}{dx} = 3 \times \left(-\frac13\right)\sin\frac x3$
$= -\sin\frac x3$ .
At $x = \frac{3\pi}{2}$ , $\frac x3 = \frac\pi2$ and $\sin\frac\pi2 = 1$ .
So $\frac{dy}{dx} = -1$ , option C.