Question

If $y=x-x^2$, then derivative of $y^2$ w.r.t. $x^2$ at $x=2$ is

• A. 1
• B. 3
• C. 5
• D. 7

Answer 1

Answer: (B)

$\frac{d\left(y^2\right)}{d\left(x^2\right)}=\frac{2y\cdot \frac{dy}{dx}}{2x}=\frac{2\left(x-x^2\right)\cdot (1-2x)}{2x}$
${\frac{d\left(y^2\right)}{d{x}^2}|}_{x=2}=\frac{(2-4)(1-4)}{2}=3$