Derivative of fx-4-x-1-x is

Given, nbsp;f(x)=4√(x)+1√(x) So, derivative will be df(x)dx=d(4√(x)+1√(x))dx=d(4x^12+x^ 12)dx ⇒ 4dx^12dx+dx^ 12dx=4×12(x^ 12) 12(x^ 32) ⇒ 2√(x) 12x√(x) ...

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Byju's Answer

Standard XII

Physics

Basic Differentiation Rule

Derivative of...

Question

Derivative of $f (x) = 4 \sqrt{x} + \frac{1}{\sqrt{x}}$ is

\frac{2}{\sqrt{x}} + \frac{1}{2 x \sqrt{x}}

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\frac{2}{\sqrt{x}} - \frac{1}{2 x \sqrt{x}}

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\frac{1}{2 x \sqrt{x}} - \frac{2}{\sqrt{x}}

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- \frac{1}{2 x \sqrt{x}} - \frac{2}{\sqrt{x}}

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Solution

The correct option is B $\frac{2}{\sqrt{x}} - \frac{1}{2 x \sqrt{x}}$
Given, $f (x) = 4 \sqrt{x} + \frac{1}{\sqrt{x}}$
So, derivative will be
$\frac{d f (x)}{d x} = \frac{d (4 \sqrt{x} + \frac{1}{\sqrt{x}})}{d x} = \frac{d (4 x^{\frac{1}{2}} + x^{\frac{- 1}{2}})}{d x}$
$\Rightarrow 4 \frac{d x^{\frac{1}{2}}}{d x} + \frac{d x^{\frac{- 1}{2}}}{d x} = 4 \times \frac{1}{2} (x^{\frac{- 1}{2}}) - \frac{1}{2} (x^{\frac{- 3}{2}})$
$\Rightarrow \frac{2}{\sqrt{x}} - \frac{1}{2 x \sqrt{x}}$

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Derivative of f(x)=4√x+1√x is

The correct option is B 2√x−12x√xGiven, f(x)=4√x+1√x So, derivative will be df(x)dx=d(4√x+1√x)dx=d(4x12+x−12)dx ⇒ 4dx12dx+dx−12dx=4×12(x−12)−12(x−32) ⇒ 2√x−12x√x

Derivative of $f (x) = 4 \sqrt{x} + \frac{1}{\sqrt{x}}$ is