en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of (3x-7)/(sqrt(x))

Solution

derivative of

\frac{3 x - 7}{x}

Solution

\frac{3 x + 7}{2 x x}

Solution steps

\frac{d}{d x} (\frac{3 x - 7}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 3 x - 7 ) x - \frac{d}{d x} ( x ) ( 3 x - 7 )}{( x ) ^{2}}

\frac{d}{d x} (3 x - 7) = 3

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

= \frac{3 x - \frac{1}{2 x} ( 3 x - 7 )}{( x ) ^{2}}

Simplify

\frac{3 x - \frac{1}{2 x} ( 3 x - 7 )}{( x ) ^{2}} : \frac{3 x + 7}{2 x x}

= \frac{3 x + 7}{2 x x}

Graph

Popular Examples

integral of 1/x sin(x)

\int \frac{1}{x} sin (x) d x

slope of y=4x-3x^2,(2,-4)

s l o p e y = 4 x - 3 x^{2}, (2, - 4)

integral of (sec^3(x))/2

\int \frac{sec ^{3} ( x )}{2} d x

limit as x approaches 0 of x^2+2x

x \to 0 lim (x^{2} + 2 x)

integral of x^{-0.5}

\int x^{- 0.5} d x

Frequently Asked Questions (FAQ)

What is the derivative of (3x-7)/(sqrt(x)) ?
The derivative of (3x-7)/(sqrt(x)) is (3x+7)/(2xsqrt(x))
What is the first derivative of (3x-7)/(sqrt(x)) ?
The first derivative of (3x-7)/(sqrt(x)) is (3x+7)/(2xsqrt(x))