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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Graph

Popular Examples

inverse oflaplace 1/(s^3+s^2+s)inverse laplace

\frac{1}{s ^{3} + s ^{2} + s}

derivative of y=x^3-sqrt(x)derivative of

y = x^{3} - x

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f (x) = cos (4 t + 12)

limit as x approaches 0 of (y^{1-x})/(1-x)

x \to 0 lim (\frac{y ^{1 - x}}{1 - x})

y^{''}-6y^'+2y=0,y(0)=0,y^'(0)=1

y^{^{''}} - 6 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 1

Frequently Asked Questions (FAQ)

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