Q 21. Find the derivatives of the func... [FREE SOLUTION]

Chapter 2: Q 21. (page 238)

Find the derivatives of the function: $f (x) = \sqrt{\sin^{- 1} x^{2}} .$

Short Answer

Expert verified

The derivative of $\sqrt{\sin^{- 1} (x^{2})} i s \frac{x}{\sqrt{\sin^{- 1} (x^{2}) - \sin^{- 1} (x^{2}) 脳 {(x)}^{4}}} .$

Step by step solution

Given information

The given expression is $f (x) = \sqrt{\sin^{- 1} (x^{2})} .$

Simplification

$f' (x) = \frac{d}{d x} (\sqrt{\sin^{- 1} (x^{2})} = \frac{1}{2 \sqrt{\sin^{- 1} (x^{2})}} 脳 \frac{d}{d x} (\sin^{- 1} (x^{2}) = \frac{1}{2 \sqrt{\sin^{- 1} (x^{2})}} 脳 \frac{1}{{1 - {(x^{2})}^{2}}} 脳 2 x = \frac{x}{\sqrt{\sin^{- 1} (x^{2}) - \sin^{- 1} (x^{2}) 脳 x^{4}}} H e n c e, f' (x) = \frac{x}{\sqrt{\sin^{- 1} (x^{2}) - \sin^{- 1} (x^{2}) 脳 x^{4}}} .$

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Find the derivatives of the function: $f (x) = \sqrt{\sin^{- 1} x^{2}} .$

Short Answer

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Find the derivatives of the function:f(x)=sin-1x2.

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Find the derivatives of the function: $f (x) = \sqrt{\sin^{- 1} x^{2}} .$