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Popular >

derivative of f(t)=(4t+8)/(t+3)

Solution

derivative of

f (t) = \frac{4 t + 8}{t + 3}

Solution

\frac{4}{( t + 3 ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{4 t + 8}{t + 3})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d t} ( 4 t + 8 ) ( t + 3 ) - \frac{d}{d t} ( t + 3 ) ( 4 t + 8 )}{( t + 3 ) ^{2}}

\frac{d}{d t} (4 t + 8) = 4

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

= \frac{4 ( t + 3 ) - 1 \cdot ( 4 t + 8 )}{( t + 3 ) ^{2}}

Simplify

\frac{4 ( t + 3 ) - 1 \cdot ( 4 t + 8 )}{( t + 3 ) ^{2}} : \frac{4}{( t + 3 ) ^{2}}

= \frac{4}{( t + 3 ) ^{2}}

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\int \frac{cos ( a x )}{sin ^{5} ( a x )} d x

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Frequently Asked Questions (FAQ)

What is the derivative of f(t)=(4t+8)/(t+3) ?
The derivative of f(t)=(4t+8)/(t+3) is 4/((t+3)^2)
What is the first derivative of f(t)=(4t+8)/(t+3) ?
The first derivative of f(t)=(4t+8)/(t+3) is 4/((t+3)^2)