JAMB 1998 · UME · Q38

If $y = 243(4x + 5)^{-2}$ , find $\frac{dy}{dx}$ when $x = 1$ .

Worked solution (try it first)

Chain rule: bring down the power $-2$ and multiply by 4, the derivative of $4x + 5$ .
So $\frac{dy}{dx} = 243 \times (-2) \times 4 \times (4x + 5)^{-3}$
$= -1944(4x + 5)^{-3}$ .
At $x = 1$ , $4x + 5 = 9$ and $9^3 = 729$ .
So $\frac{dy}{dx} = -\frac{1944}{729}$
$= -\frac83$ , option A.