## Calculus (3rd Edition)

$$\frac{d y}{d x}= -\frac{1}{3\sin \theta \cos \theta}$$ and at $\theta=\pi/4$, we have $$\frac{d y}{d x}=-\frac{2}{3}.$$
Since $x=\sin^3\theta$ and $y=\cos \theta$, then we have $$\frac{d y}{d x}= \frac{y^{\prime}}{x^{\prime}}=\frac{- \sin\theta}{3\sin^2 \theta \cos \theta}=-\frac{1}{3\sin \theta \cos \theta}$$ and at $\theta=\pi/4$, we have $$\frac{d y}{d x}=- \frac{1}{3(1/2)}=-\frac{2}{3}.$$