Given that $y = \sin^{-1}x$, show that \((\cos y)\frac{\mathrm{d}^{2}y}{\mathrm{d}x^{2}}

Question

Given that $y = \sin^{-1}x$, show that $(\cos y)\frac{\mathrm{d}^{2}y}{\mathrm{d}x^{2}} - (\sin y)\left(\frac{\mathrm{d}y}{\mathrm{d}x}\right)^{2} = 0$.

Accepted Answer

$(\cos y)\frac{\mathrm d^2y}{\mathrm dx^2}-(\sin y)\left(\frac{\mathrm dy}{\mathrm dx}\right)^2=0$

Techniques of Differentiation - Higher Derivatives by Implicit Differentiation

Techniques of Differentiation - Higher Derivatives by Implicit Differentiation

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