What is the derivative of 2x^{1/2}+x^{-1}-2 ?

The derivative of 2x^{1/2}+x^{-1}-2 is (x^2-x^{1/2})/(x^{5/2)}

What is the first derivative of 2x^{1/2}+x^{-1}-2 ?

The first derivative of 2x^{1/2}+x^{-1}-2 is (x^2-x^{1/2})/(x^{5/2)}

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

\frac{d}{d x} (2) = 0

= \frac{1}{x ^{\frac{1}{2}}} - \frac{1}{x ^{2}} - 0

Simplify

\frac{1}{x ^{\frac{1}{2}}} - \frac{1}{x ^{2}} - 0 : \frac{x ^{2} - x ^{\frac{1}{2}}}{x ^{\frac{5}{2}}}

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

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