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Popular >

derivative of f(x)=3x^{1/2}+x^{-3/2}

Solution

derivative of

f (x) = 3 x^{\frac{1}{2}} + x^{- \frac{3}{2}}

Solution

\frac{3}{2 x ^{\frac{1}{2}}} - \frac{3}{2 x ^{\frac{5}{2}}}

Solution steps

\frac{d}{d x} (3 x^{\frac{1}{2}} + x^{- \frac{3}{2}})

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (3 x^{\frac{1}{2}}) = \frac{3}{2 x ^{\frac{1}{2}}}

\frac{d}{d x} (x^{- \frac{3}{2}}) = - \frac{3}{2 x ^{\frac{5}{2}}}

= \frac{3}{2 x ^{\frac{1}{2}}} - \frac{3}{2 x ^{\frac{5}{2}}}

Graph

Popular Examples

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x \to \infty lim (x^{2} - 2 x)

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\int \frac{1}{( x + 1 ) ( x + 2 )} d x

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=3x^{1/2}+x^{-3/2} ?
The derivative of f(x)=3x^{1/2}+x^{-3/2} is 3/(2x^{1/2)}-3/(2x^{5/2)}
What is the first derivative of f(x)=3x^{1/2}+x^{-3/2} ?
The first derivative of f(x)=3x^{1/2}+x^{-3/2} is 3/(2x^{1/2)}-3/(2x^{5/2)}