Answer:
[tex]y = {tan}^{ - 1} (10x) \\tan( y) = tan({tan}^{ - 1} (10x)) \\ tany =10 x \\ {sec}^{2}(y) \frac{dy}{dx} = 10 \\ \frac{dy}{dx} = \frac{10}{{sec}^{2}(y)} \\ {sec}^{2}(y) + {tan}^{2}(y) = 10 \\ \frac{dy}{dx} = \frac{10}{{1 + tan}^{2}(y)} \\ \frac{dy}{dx} = \frac{10}{{1 + x}^{2}}[/tex]
[tex]y={sin}^{-1}(1-{x}^{2})\\ cosy \frac{dy}{dx}=-2x \\ {cos}^{2} y=\sqrt{1-{sin}^{2}y} \\ \frac{dy}{dx}=-frac{2x}{\sqrt{1-{sin}^{2}y}\\ siny=x\\ frac{dy}{dx}=-frac{2x}{\sqrt{1-{x}^{2}}[/tex]
