Question

differentiate the following w.r.t x using *chain rule*​

Answer 1

please refer the above pic

Answer 2

$\displaystyle{y=(3+x^2)^\frac{1}{2} }$

$\displaystyle{\frac{d}{dx(3+x^2)}=\frac{d}{d(3+x^2)(3+x^2)^\frac{1}{2} }.\frac{d}{dx(3+x^2)} }\\\\\\\displaystyle{=\frac{1}{2} .(3+x^2)-\frac{1}{2}.2x }$

$\displaystyle{=\frac{3+x^2}{2} -x}$