Differentiation — Maths STD 12 Science — Question

Differentiating w.r.t. $x$, we get

$\begin{aligned} & \frac{ dy }{ dx }=\frac{1}{2 \sqrt{x^2+4 x-7}} \cdot \frac{ d }{ dx }\left(x^2+4 x-7\right) \\ & =\frac{1}{2 \sqrt{x^2+4 x-7}}\left(\frac{ d }{ dx } x^2+\frac{ d }{ dx } 4 x-\frac{ d }{ dx } 7\right) \\ & =\frac{1}{2 \sqrt{x^2+4 x-7}} \cdot(2 x+4-0) \\ & =\frac{2(x+2)}{2 \sqrt{x^2+4 x-7}} \\ & =\frac{(x+2)}{\sqrt{x^2+4 x-7}} .\end{aligned}$