Differentiate the following functions with respect to x-If y-sin-1 2x1-x2-1 1-x21-x2- 0 - x - 1- prove that dydx-41-x2

y=sin^ 1 (2x1+x^2)+^ 1 (1+x^21 x^2) Putting x=tanθ we get y=2tan^ 1 x+2tan^ 1 x=4tan^ 1x Thus, dydx=41+x^2 #160; #160; #160; [Hen ...

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Differentiation of Inverse Trigonometric Functions

Differentiate...

Question

Differentiate the following functions with respect to $x$ :
If $y = {sin}^{- 1} (\frac{2 x}{1 + x^{2}}) + {sec}^{- 1} (\frac{1 + x^{2}}{1 - x^{2}}), 0 < x < 1$ , prove that $\frac{d y}{d x} = \frac{4}{1 + x^{2}}$

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\frac{d y}{d x}

y = {sin}^{- 1} (\frac{1 - x^{2}}{1 + x^{2}}), 0 < x < 1

y = \sin^{- 1} (\frac{2 x}{1 + x^{2}}) + \sec^{- 1} (\frac{1 + x^{2}}{1 - x^{2}}), 0 < x < 1,

\frac{d y}{d x} = \frac{4}{1 + x^{2}}

\frac{d y}{d x}

y = {cos}^{- 1} (\frac{1 - x^{2}}{1 + x^{2}}), 0 < x < 1

y = \sin^{- 1} (\frac{x}{1 + x^{2}}) + \cos^{- 1} (\frac{1}{\sqrt{1 + x^{2}}}), 0 < x < \infty

\frac{d y}{d x} = \frac{2}{1 + x^{2}} .

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

\sin^{- 1} (2 x \sqrt{1 - x^{2}}), if - \frac{1}{\sqrt{2}} < x < \frac{1}{\sqrt{2}}

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