en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of (x^2)/(x+8)

Solution

derivative of

\frac{x ^{2}}{x + 8}

Solution

\frac{x ^{2} + 16 x}{( x + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{x + 8})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( x + 8 ) - \frac{d}{d x} ( x + 8 ) x ^{2}}{( x + 8 ) ^{2}}

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

\frac{d}{d x} (x + 8) = 1

= \frac{2 x ( x + 8 ) - 1 \cdot x ^{2}}{( x + 8 ) ^{2}}

Simplify

\frac{2 x ( x + 8 ) - 1 \cdot x ^{2}}{( x + 8 ) ^{2}} : \frac{x ^{2} + 16 x}{( x + 8 ) ^{2}}

= \frac{x ^{2} + 16 x}{( x + 8 ) ^{2}}

Graph

Popular Examples

integral of 3sec^{-2}(xta)n^3x

\int 3 sec^{- 2} (x t a) n^{3} x d x

limit as x approaches 9 of 2x^2-3

x \to 9 lim (2 x^{2} - 3)

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

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

laplacetransform t^2cos(4t)

l a pl a ce t r an s f or m t^{2} cos (4 t)

\int ye d y

Frequently Asked Questions (FAQ)

What is the derivative of (x^2)/(x+8) ?
The derivative of (x^2)/(x+8) is (x^2+16x)/((x+8)^2)
What is the first derivative of (x^2)/(x+8) ?
The first derivative of (x^2)/(x+8) is (x^2+16x)/((x+8)^2)