en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x^2/(1+2x))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

2 x (1 + 2 x) - 2 x^{2} : 2 x + 2 x^{2}

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

Graph

Popular Examples

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

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

y^{''}+16y=16sec(4t)

y^{^{''}} + 16 y = 16 sec (4 t)

limit as x approaches 0 of cot(x)arcsin(x)

x \to 0 lim (cot (x) arcsin (x))

integral of 1/(7-2x)

\int \frac{1}{7 - 2 x} d x

(dy)/(dx)=((2y+3)^2)/((4x+5)^2)

\frac{d y}{d x} = \frac{( 2 y + 3 ) ^{2}}{( 4 x + 5 ) ^{2}}

Frequently Asked Questions (FAQ)

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