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Q.
If $y=x-x^2$, then derivative of $y^2$ w.r.t. $x^2$ at $x=2$ is
Continuity and Differentiability
Solution:
$ \frac{ d \left( y ^2\right)}{ d \left( x ^2\right)}=\frac{2 y \cdot \frac{ dy }{ dx }}{2 x }=\frac{2\left( x - x ^2\right) \cdot(1-2 x )}{2 x }$
$\left.\frac{ d \left( y ^2\right)}{ dx ^2}\right|_{ x =2}=\frac{(2-4)(1-4)}{2}=3$