Question

Find $\frac{dy}{dx}$ for the curve $x^2=y$ at the point $(1,1)$.

Answer 1

Given curve, $x^2=y$

Differentiate on both sides w.r.t $x$

$\frac{d}{dx}\left(x^2\right)=\frac{dy}{dx}$

$\frac{dy}{dx}=2x$

Therefore, $\frac{dy}{dx}$ at $(1,1)$ $=2\left(1\right)=2$