Question

$d/dx\log \left(\sqrt{(x-}a\right)+\sqrt{(x-b}\left)\right)=$

• A. $1/2\sqrt{(x-a})+\sqrt{(x-b})$
• B. $1/2(\sqrt{\left(x-a\right)}+\sqrt{(x-b)})$
• C. $1/\sqrt{(x-a)}+\sqrt{(x-b)}$
• D. $noneofthese$

Answer 1

The correct option is B

$1/2(\sqrt{\left(x-a\right)}+\sqrt{(x-b)})$

Finding the value of

Given,

$y=\log \left(\sqrt{\left(x-a\right)+\left(x-b\right)}\right)$

Differentiate with respect to ‘x’.

$$\begin{gathered} \frac{dy}{dx}=[1/(\sqrt{(x-a)}+\sqrt{(x-b)})](1/2)\sqrt{(x-a)}+(1/2)\sqrt{(x-b)} \\ =[1/2(\sqrt{(x-a)}+\sqrt{(x-b)})]\left[\right(\sqrt{(x-b)}+\sqrt{(x-a)})/\sqrt{(x-a)}]\sqrt{(x-b)} \\ =1/2\sqrt{(x-a)\surd (x-b)} \\ \mathbf{}\mathbf{=}\mathbf{}\mathbf{1}\mathbf{/}\mathbf{2}\sqrt{\mathbf{\left(}\mathbf{\right(}\mathbf{x}\mathbf{-}\mathbf{a}\mathbf{\left)}\mathbf{\right(}\mathbf{x}\mathbf{-}\mathbf{b}\mathbf{\left)}\mathbf{\right)}} \end{gathered}$$

Hence option(B) is correct.