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Popular >

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

Solution

derivative of

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

Solution

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

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

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

Popular Examples

integral of 4/(16+x^2)

\int \frac{4}{16 + x ^{2}} d x

integral of sin^4(v)cos^3(v)

\int sin^{4} (v) cos^{3} (v) d v

xy^'+y=2xy^2,y(1)=-5

x y^{^{'}} + y = 2 x y^{2}, y (1) = - 5

(\partial)/(\partial x)(e^ysin(xy))

\frac{\partial}{\partial x} (e^{y} sin (x y))

derivative of (12x^2-x^4/((4-x^2)^2))

\frac{d}{d x} (\frac{12 x ^{2} - x ^{4}}{( 4 - x ^{2} ) ^{2}})

Frequently Asked Questions (FAQ)

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