(i) Match the following d/dx (sinx),d/dx (e^cosx) d/dx(sin^-1)(2x/1+x^2) d/dx (sin^-1 (x))

Question

(i) Match the following.

A	B
\(\frac{d}{dx}(sin x)\)	-cosx
\(\frac{d}{dx}(e^{cos x})\)	\(\frac{2}{1 + x^2}\)
\(\frac{d}{dx}(sin ^{-1}(\frac{2x}{1+x^2}))\)	-sin x. ecos x
\(\frac{d}{dx}((sin ^{-1}x))\)	cos x
	\(\frac{1}{\sqrt{(1-x^2)}}\)

(ii) If y = sin^-1 x, prove that (1 – x²) y₂ – xy₁ = 0

Answer 1

(ii) Given y = sin^-1 x,

Differentiating w.r.t. x,