Step 1 — Differentiate $x$ with respect to $t$.

$$x = a\sin^3 t$$

Using the chain rule:

$$\frac{dx}{dt} = 3a\sin^2 t\cos t$$

Step 2 — Differentiate $y$ with respect to $t$.

$$y = b\cos^3 t$$

$$\frac{dy}{dt} = 3b\cos^2 t \cdot (-\sin t) = -3b\cos^2 t\sin t$$

Step 3 — Form $\dfrac{dy}{dx}$ using the parametric rule.

$$\frac{dy}{dx} = \frac{dy/dt}{dx/dt} = \frac{-3b\cos^2 t\sin t}{3a\sin^2 t\cos t}$$

Step 4 — Cancel the common factors.

Cancelling $3$, one $\cos t$ and one $\sin t$:

$$\frac{dy}{dx} = -\frac{b\cos t}{a\sin t} = -\frac{b}{a}\cot t$$

Step 5 — Substitute $t = \dfrac{\pi}{4}$.

$$\cot\frac{\pi}{4} = 1$$

$$\frac{dy}{dx}\bigg|_{t = \pi/4} = -\frac{b}{a}(1)$$

$$\boxed{\frac{dy}{dx} = -\frac{b}{a}}$$