en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of (2t+1)/(t+3)

Solution

derivative of

\frac{2 t + 1}{t + 3}

Solution

\frac{5}{( t + 3 ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{2 t + 1}{t + 3})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{5}{( t + 3 ) ^{2}}

Graph

Popular Examples

derivative of 8x+9xe^x

d er i v a t i v e 8 x + 9 x e^{x}

integral of cos((npix)/L)

\int cos (\frac{nπ x}{L}) d x

derivative of 3^{2x^2}*sqrt(x)

\frac{d}{d x} (3^{2 x^{2}} \cdot x)

derivative of (10/(x^2+1))

\frac{d}{d x} (\frac{10}{x ^{2} + 1})

limit as x approaches-4 of 1/2 x-1

x \to - 4 lim (\frac{1}{2} x - 1)

Frequently Asked Questions (FAQ)

What is the derivative of (2t+1)/(t+3) ?
The derivative of (2t+1)/(t+3) is 5/((t+3)^2)
What is the first derivative of (2t+1)/(t+3) ?
The first derivative of (2t+1)/(t+3) is 5/((t+3)^2)