First slide

Derivatives

Question

$If y = \frac{(a - x) \sqrt{a - x} - (b - x) \sqrt{x - b}}{\sqrt{a - x} + \sqrt{x - b}} then \frac{d y}{d x} whenever it is defined is$

Moderate

A

$\frac{x + (a + b)}{\sqrt{(a - x) (x - b)}}$
B

$\frac{2 x - a - b}{2 \sqrt{a - x} \sqrt{x - b}}$
C

$- \frac{(a + b)}{2 \sqrt{(x - x) (x - b)}}$
D

$\frac{2 x + (a + b)}{2 \sqrt{(a - x) (x - b)}}$

Solution

$y = \frac{{(a - x)}^{3 / 2} + {(x - b)}^{3 / 2}}{\sqrt{a - x} + \sqrt{x - b}}$
$\begin{array}{l} = \frac{(\sqrt{a - x} + \sqrt{x - b}) (a - x - \sqrt{a - x} \sqrt{x - b} + x - b)}{\sqrt{a - x} + \sqrt{x - b}} \\ = a - b - \sqrt{a - x} \sqrt{x - b} \\ \frac{d y}{d x} = \frac{1}{2 \sqrt{a - x}} \sqrt{x - b} - \frac{1}{2 \sqrt{x - b}} \sqrt{a - x} \\ = \frac{2 x - a - b}{2 \sqrt{a - x} \sqrt{x - b}} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App