(i) Match the following A :- d/dx(x), d/dx(8), d/dx cos^-1x

Question

(i) Match the following.

A	B
\(\frac{d}{dx}(x)\)	0
\(\frac{d}{dx}(8)\)	\(\frac{1}{2\sqrt{x}}\)
\(\frac{d}{dx}cos^{-1}x\)	1
\(\frac{d}{dx}\sqrt{x}\)	\(\frac{-1}{\sqrt{1-x^2}}\)
	2\(\sqrt{x}\)

(ii) If y = e^{a cos-1x}, then show that (1 – x²)y₂ – xy₁ – a²y = 0 

Answer 1

(i) 

A	B
\(\frac{d}{dx}(x)\)	1
\(\frac{d}{dx}(8)\)	0
\(\frac{d}{dx}cos^{-1}x\)	\(\frac{-1}{\sqrt{1-x^2}}\)
\(\frac{d}{dx}\sqrt{x}\)	\(\frac{1}{2\sqrt{x}}\)

 (ii) Given, 

y = e^{a cos-1x} ____(1)

Differentiating w.r.to x,

Again differentiating w. r. t to x

⇒ (1 – x²)y₂ – xy₁ = a². e^{a cos-1x}

⇒ (1 – x²)y₂ – xy₁ = a²y

⇒ (1 – x²)y₂ – xy₁ – a²y = 0.