Suppose $y = \sin(-3 x^2+ x - 3 )$. We can write $y = \sin(u)$, where $u =$ . The Leibnitz notation for the chain rule is $\displaystyle \frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}$. The factors are $\displaystyle \frac{dy}{du} =$ (written as a function of $u$ ) and $\displaystyle \frac{du}{dx} =$ . Now substitue in the function of $x$ for $u$ to get

$\displaystyle \frac{dy}{dx} =$ (written as a function of $x$ ).