Implicit differentiation and inverse trigonometric functions practice question 18

Differentiate both sides with respect to $x$. The term $xy^{2}$ is a product of $x$ and $y^{2}$, and $e^{y}$ needs the chain rule.

The product rule gives $\dfrac{d}{dx}\bigl(xy^{2}\bigr) = y^{2} + x\cdot 2y\,\dfrac{dy}{dx}$. Then move every term containing $\dfrac{dy}{dx}$ to one side, factor it out, and divide.