Differential coefficient of $\sec^{- 1}\frac{1}{2x^{2} - 1}\ with\ respect\ to\ \sqrt{1 - x^{2}}\ at\ x = \frac{1}{2}$ is equal to

Question

Dr. Abubacker · Accepted Answer

(b)
Let $y_{1} = \sec^{- 1}{\frac{1}{2x^{2} - 1}\ \ \ and\ {\ \ \ \ \ \ y}_{2} = \sqrt{1 - x^{2}}}$
$\Rightarrow$ $\frac{dy_{1}}{dx} = \frac{- 2}{\sqrt{1 - x^{2}}}\ \ and\ \ \ \frac{dy_{2}}{dx} = \frac{- x}{\sqrt{1 - x^{2}}}$
$\Rightarrow \frac{dy_{1}}{dy_{2}} = \frac{2}{x}\ \ \  \Rightarrow \ \ \ \left( \frac{dy_{1}}{dy_{2}} \right)_{x = 1/2} = 4$

Q. Differential coefficient of $\sec^{- 1}\frac{1}{2x^{2} - 1}\ with\ respect\ to\ \sqrt{1 - x^{2}}\ at\ x = \frac{1}{2}$ is equal to

Explanation

Reviewed by Dr. Abubacker

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