en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x+3/(x-2))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot ( x - 2 ) - 1 \cdot ( x + 3 )}{( x - 2 ) ^{2}} : - \frac{5}{( x - 2 ) ^{2}}

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

Popular Examples

(\partial)/(\partial x)(xy^3+2xy)

\frac{\partial}{\partial x} (x y^{3} + 2 x y)

limit as x approaches infinity of tan((2xpi)/(1+8x))

x \to \infty lim (tan (\frac{2 x π}{1 + 8 x}))

integral of 1/(sqrt(36x^2-49))

\int \frac{1}{36 x ^{2} - 49} d x

derivative of (4x/((x^2+2)^2))

\frac{d}{d x} (\frac{4 x}{( x ^{2} + 2 ) ^{2}})

(\partial)/(\partial z)(x^2+y^2+z^2)

\frac{\partial}{\partial z} (x^{2} + y^{2} + z^{2})

Frequently Asked Questions (FAQ)

What is the derivative of (x+3/(x-2)) ?
The derivative of (x+3/(x-2)) is -5/((x-2)^2)
What is the first derivative of (x+3/(x-2)) ?
The first derivative of (x+3/(x-2)) is -5/((x-2)^2)