Question

Find $dy/dx$ at $x=4$ if $\sqrt{x}+\sqrt{y}=4,$
find absolute value of ans

Answer 1

Given, $\sqrt{x}+\sqrt{y}=4,$
Differentiating both sides w.r.t. x, we get
$\frac{1}{2\sqrt{\left(x\right)}}+\frac{1}{2\sqrt{\left(y\right)}}=0\therefore \frac{dy}{dx}=-\sqrt{\left(\frac{x}{y}\right)}$.
Clearly at $y=4,x=4$
Therefore absolute value of $\frac{dy}{dx}$ at $(4,4)$ is 1.