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Popular >

derivative of 2/x+sqrt(x)

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

- \frac{2}{x ^{2}} + \frac{1}{2 x} : \frac{- 4 + x ^{\frac{3}{2}}}{2 x ^{\frac{3}{2}} x}

= \frac{- 4 + x ^{\frac{3}{2}}}{2 x ^{\frac{3}{2}} x}

Popular Examples

(\partial)/(\partial v)(1/(u^2+v^2))

\frac{\partial}{\partial v} (\frac{1}{u ^{2} + v ^{2}})

integral of (7+6x)/(1+x^2)

\int \frac{7 + 6 x}{1 + x ^{2}} d x

limit as x approaches 3 of 2x-5

x \to 3 lim (2 x - 5)

limit as x approaches pi/x of xcos(x)

x \to \frac{π}{x} lim (x cos (x))

limit as x approaches-2 of \sqrt[3]{x+2}

Frequently Asked Questions (FAQ)

What is the derivative of 2/x+sqrt(x) ?
The derivative of 2/x+sqrt(x) is (-4+x^{3/2})/(2x^{3/2)sqrt(x)}
What is the first derivative of 2/x+sqrt(x) ?
The first derivative of 2/x+sqrt(x) is (-4+x^{3/2})/(2x^{3/2)sqrt(x)}