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

Question

Given that $y={{({{\sin }^{-1}}x)}^{2}}$, show that $(1-{{x}^{2}}){{\left(\frac{\mathrm{d}y}{\mathrm{d}x} \right)}^{2}}=4y$ and $(1-{{x}^{2}})\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d}{{x}^{2}}}-x\frac{\mathrm{d}y}{\mathrm{d}x}=2$.

Accepted Answer

$(1-x^2)\left(\frac{\mathrm dy}{\mathrm dx}\right)^2=4y$ $(1-x^2)\frac{\mathrm d^2y}{\mathrm dx^2}-x\frac{\mathrm dy}{\mathrm dx}=2$

Techniques of Differentiation - Derivatives of Inverse Trigonometric Functions

Techniques of Differentiation - Derivatives of Inverse Trigonometric Functions

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