en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of f(x)=3x^{1/2}+x^{-3/2}

Solution

derivative of

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

Solution

\frac{3}{2 x ^{\frac{1}{2}}} - \frac{3}{2 x ^{\frac{5}{2}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (x^{- \frac{3}{2}}) = - \frac{3}{2 x ^{\frac{5}{2}}}

= \frac{3}{2 x ^{\frac{1}{2}}} - \frac{3}{2 x ^{\frac{5}{2}}}

Graph

Popular Examples

tangent of y=x^2-6x+9,(3,0)

t an g e n t y = x^{2} - 6 x + 9, (3, 0)

limit as x approaches infinity of x^2-2x

x \to \infty lim (x^{2} - 2 x)

integral of 1/((x+1)(x+2))

\int \frac{1}{( x + 1 ) ( x + 2 )} d x

integral of 1/(x\sqrt[3]{ln(x)-1)}

\int \frac{1}{x 3 ln ( x ) - 1} d x

integral from-2 to 1 of (-2x+3)

\int_{- 2}^{1} (- 2 x + 3) d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=3x^{1/2}+x^{-3/2} ?
The derivative of f(x)=3x^{1/2}+x^{-3/2} is 3/(2x^{1/2)}-3/(2x^{5/2)}
What is the first derivative of f(x)=3x^{1/2}+x^{-3/2} ?
The first derivative of f(x)=3x^{1/2}+x^{-3/2} is 3/(2x^{1/2)}-3/(2x^{5/2)}