Answer
$\frac{dy}{dz}=cos^{-1}{z}$
Work Step by Step
Given $y=zcos^{-1}{z}-\sqrt{(1-z^2)}$
On differentiating both sides:
$\frac{dy}{dz}=\frac{d(zcos^{-1}{z}-\sqrt{(1-z^2)})}{dz}$
$\frac{dy}{dz}=z{\frac{-1}{\sqrt{(1-z^2)}}}+cos^{-1}{z}-\frac{1}{2\sqrt{(1-z^2)}}\frac{d({(1-z^2)})}{dz}$
$\frac{dy}{dz}={\frac{-z}{\sqrt{(1-z^2)}}}+cos^{-1}{z}+\frac{z}{\sqrt{(1-z^2)}}$
$\frac{dy}{dz}=cos^{-1}{z}$
