Question

If $f\left(x\right)=\sqrt{x^2+1},g\left(x\right)=\frac{x+1}{x^2+1}$ and $h\left(x\right)=2x-3,$ then find $f^{\prime }\left[h^{\prime }|g^{\prime }\right(x\left)|\right]$.

Answer 1

$f^{{}^{\prime }}\left(x\right)=\frac{x}{\sqrt{x^2+1}}$

$h^{{}^{\prime }}\left(x\right)=2$

Hence, irrespective of $g^{{}^{\prime }}\left(x\right)$, $h^{{}^{\prime }}\left(x\right)$ will be constant.

Thus, the required solution is

$f^{{}^{\prime }}\left(2\right)=\frac{2}{\sqrt{5}}$