If $y=x-x^2$, then the rate of change of $y^2$ with respect to $x^2$ at $x=2$ is

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Aicharya · Accepted Answer

$y=x-x^2$ Let $v=y^2=x^2+x^4-2 x^3 \Rightarrow \frac{d\left(y^2\right)}{d x}=2 x+4 x^3-6 x^2$ $u=x^2 \Rightarrow \frac{d u}{d x}=2 x$ $\frac{d v}{d u}=\frac{d v / d x}{d u / d x}=1+2 x^2-\left.3 x \Rightarrow \frac{d\left(y^2\right)}{d\left(x^2\right)}\right|_{x=2}=1+8-6=3$

If $y=x-x^2$, then the rate of change of $y^2$ with respect to $x^2$ at $x=2$ is

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