What is the derivative of ((x^2+3x-4)/(x+2)) ?

The derivative of ((x^2+3x-4)/(x+2)) is (x^2+4x+10)/((x+2)^2)

What is the first derivative of ((x^2+3x-4)/(x+2)) ?

The first derivative of ((x^2+3x-4)/(x+2)) is (x^2+4x+10)/((x+2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{( x ^{2} + 3 x - 4 )}{x + 2})

\frac{x ^{2} + 4 x + 10}{( x + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{( x ^{2} + 3 x - 4 )}{x + 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} + 3 x - 4 ) ( x + 2 ) - \frac{d}{d x} ( x + 2 ) ( x ^{2} + 3 x - 4 )}{( x + 2 ) ^{2}}

\frac{d}{d x} (x^{2} + 3 x - 4) = 2 x + 3

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

= \frac{( 2 x + 3 ) ( x + 2 ) - 1 \cdot ( x ^{2} + 3 x - 4 )}{( x + 2 ) ^{2}}

Simplify

\frac{( 2 x + 3 ) ( x + 2 ) - 1 \cdot ( x ^{2} + 3 x - 4 )}{( x + 2 ) ^{2}} : \frac{x ^{2} + 4 x + 10}{( x + 2 ) ^{2}}

= \frac{x ^{2} + 4 x + 10}{( x + 2 ) ^{2}}

\frac{d}{d x} (- cos (x) - sin (x))

\frac{1}{y} y^{^{'}} = - \frac{1}{x}

y^{^{''}} + 3 y^{^{'}} + 2 y = sin^{2} (t)

y^{^{''}} + 14 y^{^{'}} + 50 y = 0

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

What is the derivative of ((x^2+3x-4)/(x+2)) ?
The derivative of ((x^2+3x-4)/(x+2)) is (x^2+4x+10)/((x+2)^2)
What is the first derivative of ((x^2+3x-4)/(x+2)) ?
The first derivative of ((x^2+3x-4)/(x+2)) is (x^2+4x+10)/((x+2)^2)