Choose the correct answer. If f(x)= x +1 x then dy dx at x = 1 is… - Vidyadip

MCQ

Choose the correct answer. If $\text{f}(\text{x})=\sqrt{\text{x}}+\frac{1}{\sqrt{\text{x}}}$ then $\frac{\text{dy}}{\text{dx}}$ at $x = 1$ is equal to:

A
$1$
B
$\frac{1}{2}$
C
$\frac{1}{\sqrt{2}}$
✓
$0$

✓

Answer

Correct option: D.

$0$

Given that $\text{f}(\text{x})=\sqrt{\text{x}}+\frac{1}{\sqrt{\text{x}}}$
$\frac{\text{dy}}{\text{dx}}=\frac{1}{2\sqrt{\text{x}}}-\frac{1}{2\text{x}^{\frac{3}{2}}}$
$\big(\frac{\text{dy}}{\text{dx}}\big)=\frac{1}{2}-\frac{1}{2}=0$

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