What is the derivative of x^{0.5}+2x^{-0.5} ?

The derivative of x^{0.5}+2x^{-0.5} is (0.5x-1)/(x^{1.5)}

What is the first derivative of x^{0.5}+2x^{-0.5} ?

The first derivative of x^{0.5}+2x^{-0.5} is (0.5x-1)/(x^{1.5)}

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\frac{d}{d x} (x^{0.5} + 2 x^{- 0.5})

\frac{0.5 x - 1}{x ^{1.5}}

Solution steps

\frac{d}{d x} (x^{0.5} + 2 x^{- 0.5})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{0.5}) + \frac{d}{d x} (2 x^{- 0.5})

\frac{d}{d x} (x^{0.5}) = \frac{0.5}{x ^{0.5}}

\frac{d}{d x} (2 x^{- 0.5}) = - \frac{1}{x ^{1.5}}

= \frac{0.5}{x ^{0.5}} - \frac{1}{x ^{1.5}}

Simplify

\frac{0.5}{x ^{\frac{1}{2}}} - \frac{1}{x ^{1.5}} : \frac{0.5 x - 1}{x ^{1.5}}

= \frac{0.5 x - 1}{x ^{1.5}}

(2.6) (- 3.5)

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\int \frac{2 - x}{4 x ^{2} + 4 x - 3} d x

\frac{d y}{d x} + x^{2} (3 y - 2) = 0

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What is the derivative of x^{0.5}+2x^{-0.5} ?
The derivative of x^{0.5}+2x^{-0.5} is (0.5x-1)/(x^{1.5)}
What is the first derivative of x^{0.5}+2x^{-0.5} ?
The first derivative of x^{0.5}+2x^{-0.5} is (0.5x-1)/(x^{1.5)}