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Popular >

derivative of f(x)=sqrt(x)+1/x

Solution

derivative of

f (x) = x + \frac{1}{x}

Solution

\frac{x ^{\frac{3}{2}} - 2}{2 x ^{\frac{3}{2}} x}

Solution steps

\frac{d}{d x} (x + \frac{1}{x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x) + \frac{d}{d x} (\frac{1}{x})

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

= \frac{1}{2 x} - \frac{1}{x ^{2}}

Simplify

\frac{1}{2 x} - \frac{1}{x ^{2}} : \frac{x ^{\frac{3}{2}} - 2}{2 x ^{\frac{3}{2}} x}

= \frac{x ^{\frac{3}{2}} - 2}{2 x ^{\frac{3}{2}} x}

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x \to a + lim (\frac{cos ( x ) ln ( x - a )}{ln ( e ^{x} - e ^{a} )})

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\frac{d}{d x} (x e^{(- 2 x^{2})})

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∣ x ∣, \frac{x}{2} + 3

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(x)+1/x ?
The derivative of f(x)=sqrt(x)+1/x is (x^{3/2}-2)/(2x^{3/2)sqrt(x)}
What is the first derivative of f(x)=sqrt(x)+1/x ?
The first derivative of f(x)=sqrt(x)+1/x is (x^{3/2}-2)/(2x^{3/2)sqrt(x)}