Derivative of sin -1 x w-r-t- cos -1-1-x2 is

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Integration by Substitution

Derivative of...

Question

${Derivative of sin}^{- 1} x w . r . t . c o s^{- 1} \sqrt{1 - x^{2}} i s$

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-1

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{sin}^{- 1} x

{cos}^{- 1} \sqrt{1 - x^{2}}

- 1 \leq x \leq 1

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

{cos}^{- 1} (\frac{1 - x^{2}}{1 + x^{2}})

1,

0 < x < 1

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

- 1 \leq x \leq 1

The derivative of ${sin}^{- 1} (\frac{2 x}{1 + x^{2}})$ w.r.t ${sin}^{- 1} (\frac{1 - x^{2}}{1 + x^{2}})$ is

{tan}^{- 1} \frac{cos x - sin x}{cos x + sin x}

x

f (x) = {cos}^{- 1} {\frac{1}{\sqrt{13}} (2 cos x - 3 sin x)} + {sin}^{- 1} {\frac{1}{\sqrt{13}} (2 cos x + 3 sin x)}

\sqrt{1 + x^{2}}

x = \frac{3}{4}

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