First slide

Derivatives

Question

$If f (x) = \sqrt{a x} + \frac{a^{2}}{\sqrt{a x}} then f^{'} (a) =$

Moderate

A

0
B

1
C

-1
D

a

Solution

$\begin{array}{l} f^{'} (x) = \frac{a}{2 \sqrt{a x}} + a^{2} [\frac{- 1}{2} (a x)^{- 1 / 2 - 1}] a \\ f^{'} (a) = \frac{a}{2 \sqrt{a^{2}}} + a^{2} [\frac{- 1}{2} {(a^{2})}^{- 3 / 2}] a \\ = \frac{1}{2} + a^{2} (- \frac{1}{2} \frac{1}{a^{3}}) a \\ = \frac{1}{2} - \frac{1}{2} = 0 \end{array}$

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