Question

if $y=x^2$
then $\frac{dy}{dx}$ is equal to

• A. $\frac{2xy}{2y-x^2}$
• B. $\frac{xy}{2y-x^2}$
• C. $\frac{xy}{y-x^2}$
• D. $\frac{2xy}{2+\frac{x^2}{y}}$

Answer 1

The correct option is A $\frac{2xy}{2y-x^2}$

$y=x^2+\frac{1}{y}$

$\Rightarrow y^2=x^{2}y+1$

Differentiating both sides

$2y\frac{dy}{dx}=2xy+x^2\frac{dy}{dx}$

$\Rightarrow (2y-x^2)\frac{dy}{dx}=2xy$

$\Rightarrow \frac{dy}{dx}=\frac{2xy}{2y-x^2}$