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Popular >

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

Solution

derivative of

f (t) = \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

integral of (x^2)/(sqrt(1-x^3))

\int \frac{x ^{2}}{1 - x ^{3}} d x

integral of 2/(sqrt(x^2+16))

\int \frac{2}{x ^{2} + 16} d x

integral from 2 to infinity of 5/(x^2)

\int_{2}^{\infty} \frac{5}{x ^{2}} d x

integral of 9/(xsqrt(4-81ln^2(x)))

\int \frac{9}{x 4 - 81 ln ^{2} ( x )} d x

integral of sqrt(50-x/2)

\int 50 - \frac{x}{2} d x

Frequently Asked Questions (FAQ)

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