If y- sin -12x-1-x2- -11- 1-x2 - then dy-dx- at x-0 is

y= sin ^ 12x√(1 x^2)+ ^ 11/√( ( 1 x^2 )), Put x= sinθ , then y= 2θ +θ =3θ =3sin^ 1x ⇒ nbsp; dy/dx= 3/√( ( 1 x^2 ))∴ y'(0) = 3 ...

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Functions

If y= sin -...

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If $y = {sin}^{- 1} 2 x \sqrt{1 - x^{2}} + {sec}^{- 1} \frac{1}{\sqrt{(1 - x^{2})}},$ then $\frac{d y}{d x} .$ at $x = 0$ is

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

\frac{d y}{d x}

y = {sin}^{- 1} (2 x \sqrt{1 - x^{2}}), - \frac{1}{\sqrt{2}} \leq x \leq \frac{1}{\sqrt{2}}

\frac{d y}{d x}

y = {sin}^{- 1} \frac{2 x}{1 + x^{2}} + {sec}^{- 1} \frac{1 + x^{2}}{1 - x^{2}},

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

y = {sin}^{- 1} \frac{1}{\sqrt{1 + x^{2}}} + {tan}^{- 1} (\frac{\sqrt{1 + x^{2}} - 1}{x})

\frac{d y}{d x}

(x \neq 0)

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

\frac{d y}{d x}

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