en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

derivative of

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

Solution

\frac{9}{( t + 3 ) ^{2}}

Solution steps

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

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

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

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

Simplify

\frac{3 ( t + 3 ) - 1 \cdot ( 2 t + t )}{( t + 3 ) ^{2}} : \frac{9}{( t + 3 ) ^{2}}

= \frac{9}{( t + 3 ) ^{2}}

Popular Examples

derivative of xsin(xtan(x))

\frac{d}{d x} (x sin (x) tan (x))

derivative of (x^{3/2}-4x(x^4-3/(x^2)+2))

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

derivative of sqrt(4x+2)derivative of

4 x + 2

derivative of (2x^2+5x+8/(2x^2))

\frac{d}{d x} (\frac{2 x ^{2} + 5 x + 8}{2 x ^{2}})

integral of 1/((sec(x))^2)

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

Frequently Asked Questions (FAQ)

What is the derivative of (2t+t)/(t+3) ?
The derivative of (2t+t)/(t+3) is 9/((t+3)^2)
What is the first derivative of (2t+t)/(t+3) ?
The first derivative of (2t+t)/(t+3) is 9/((t+3)^2)