Question

If $y=x-x^2$ then the derivative of $y^2$ wrt to $x^2$ is

• A. $2x^2+3x-1$
• B. $2x^2-3x+1$
• C. $2x^2+3x+1$
• D. None of these

Answer 1

The correct option is B $2x^2-3x+1$

$y=x-x^2\Rightarrow y^2={(x-x^2)}^2$
$\frac{d}{dx}\left(y^2\right)=\frac{d}{dx}\left({(x-x^2)}^2\right)=2(x-x^2)(1-2x)$
$\frac{d\left(x^2\right)}{dx}=2x$

Using $\frac{d\left(y^2\right)}{d\left(x^2\right)}=\frac{d\left(y^2\right)}{dx}÷\frac{d\left(x^2\right)}{dx}$
Therefore derivative of $y^2$ w.r.t $x^2$ is
$=\frac{2(x-x^2)(1-2x)}{2x}={2x}^2-3x+1$