en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x/(2x+5)

Solution

\frac{d}{d x} (\frac{x}{2 x + 5})

Solution

\frac{5}{( 2 x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{2 x + 5})

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} (2 x + 5) = 2

= \frac{1 \cdot ( 2 x + 5 ) - 2 x}{( 2 x + 5 ) ^{2}}

Simplify

= \frac{5}{( 2 x + 5 ) ^{2}}

Popular Examples

derivative of (1+sqrt(x)^3)

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

integral from 1 to 3 of (x^2+7)/(4x-x^2)

\int_{1}^{3} \frac{x ^{2} + 7}{4 x - x ^{2}} d x

(\partial)/(\partial x)(2xye^{-x^2-y^2})

\frac{\partial}{\partial x} (2 x y e^{- x^{2} - y^{2}})

derivative of 6sec(xtan(x))

\frac{d}{d x} (6 sec (x) tan (x))

integral from 0 to infinity of e^{x/3}

\int_{0}^{\infty} e^{\frac{x}{3}} d x

Frequently Asked Questions (FAQ)

What is the derivative of x/(2x+5) ?
The derivative of x/(2x+5) is 5/((2x+5)^2)
What is the first derivative of x/(2x+5) ?
The first derivative of x/(2x+5) is 5/((2x+5)^2)