Question

Find the derivative of a & b (see attachment)

Answer 1

`y = {tan}^( - 1) (10x) \\tan( y) = tan({tan}^( - 1) (10x)) \\ tany =10 x \\ {sec}^(2)(y) (dy)/(dx) = 10 \\ (dy)/(dx) = \frac{10}{{sec}^(2)(y)} \\ {sec}^(2)(y) + {tan}^(2)(y) = 10 \\ (dy)/(dx) = \frac{10}{{1 + tan}^(2)(y)} \\ (dy)/(dx) = \frac{10}{{1 + x}^(2)}`

`y={sin}^(-1)(1-{x}^(2))\\ cosy (dy)/(dx)=-2x \\ {cos}^(2) y=\sqrt{1-{sin}^(2)y} \\ (dy)/(dx)=-frac{2x}{\sqrt{1-{sin}^(2)y}\\ siny=x\\ frac{dy}{dx}=-frac{2x}{\sqrt{1-{x}^(2)}`