The correct option is A 1|x| √( ( x^2 1 )) Let, #160; y = ^ 1 x⇒ y = x Differentiating both side w.r.t x y.tan y dydx=1 dydx= 1 y√( ...

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Differentiation of Inverse Trigonometric Functions

Differentiate...

Question

Differentiate ${sec}^{- 1} x$

\frac{1}{| x | \sqrt{(x^{2} - 1)}}

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\frac{1}{| x | \sqrt{(x^{2} + 1)}}

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\frac{1}{x \sqrt{(x^{2} - 1)}}

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\frac{- 1}{x \sqrt{(x^{2} - 1)}}

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Solution

The correct option is A $\frac{1}{| x | \sqrt{(x^{2} - 1)}}$
Let, $y = {sec}^{- 1} x \Rightarrow sec y = x$
Differentiating both side w.r.t $x$
$sec y . tan y \frac{d y}{d x} = 1$
$\frac{d y}{d x} = \frac{1}{sec y \sqrt{({sec}^{2} y - 1)}} = \frac{1}{| x | \sqrt{(x^{2} - 1)}}$

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Similar questions

{tan}^{- 1} \frac{\sqrt{1 + x^{2}} - 1}{x}

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Solveis equal to

(A) (B) (C) (D)

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