What is the derivative of ((x^2+3))/((x+1)) ?

The derivative of ((x^2+3))/((x+1)) is (x^2+2x-3)/((x+1)^2)

What is the first derivative of ((x^2+3))/((x+1)) ?

The first derivative of ((x^2+3))/((x+1)) is (x^2+2x-3)/((x+1)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

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

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

Solution steps

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

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

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

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

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

Simplify

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

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

d er i v a t i v e 2 tan (x) + sec (x) - 3 cot (x)

d er i v a t i v e \frac{x ^{3}}{3 - 3 x}

d er i v a t i v e 3^{x} + 2

d er i v a t i v e lo g_{10} (\frac{2}{x})

d er i v a t i v e \frac{( 3 x ^{2} - 1 ) ^{2}}{( x + 1 ) ^{3}}

What is the derivative of ((x^2+3))/((x+1)) ?
The derivative of ((x^2+3))/((x+1)) is (x^2+2x-3)/((x+1)^2)
What is the first derivative of ((x^2+3))/((x+1)) ?
The first derivative of ((x^2+3))/((x+1)) is (x^2+2x-3)/((x+1)^2)