Question

differtiation of √x+1/x​

Answer 1

Answer:

√x+1/x

x√x+1/x=0

x√x+1=0

x√x=-1

x=-1/√x

x=-√x/x

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Answer 2

Answer:

$\large\boxed{\sf{ \frac{1}{2 \sqrt{x} } (1 - \frac{1}{ x} )}}$

Step-by-step explanation:

$\frac{d}{dx} ( \sqrt{x} + \frac{1}{ \sqrt{x} } ) \\ \\ = \frac{d}{dx} \sqrt{x} + \frac{d}{dx} \frac{1}{ \sqrt{x} } \\ \\ = \frac{d}{dx} {x}^{ \frac{1}{2} } + \frac{d}{dx} {x}^{ - \frac{1}{2} } \\ \\ = \frac{1}{2} {x}^{ \frac{1}{2} - 1} - \frac{1}{2} {x}^{ - \frac{ 1}{2} - 1} \\ \\ = \frac{1}{2} {x}^{ - \frac{1}{2} } - \frac{1}{2} {x}^{ - \frac{3}{2} } \\ \\ = \frac{1}{2 \sqrt{x} } - \frac{1}{2x \sqrt{x} } \\ \\ = \frac{1}{2 \sqrt{x} } (1 - \frac{1}{ x} )$

Concept Map :-

• $\dfrac{d}{dx} {x}^{n} = n {x}^{n - 1}$