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Popular >

derivative of G(t)=(1-2t)/(3+t)

Solution

derivative of

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

Solution

- \frac{7}{( 3 + t ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( - 2 ) ( 3 + t ) - 1 \cdot ( 1 - 2 t )}{( 3 + t ) ^{2}} : - \frac{7}{( 3 + t ) ^{2}}

= - \frac{7}{( 3 + t ) ^{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of G(t)=(1-2t)/(3+t) ?
The derivative of G(t)=(1-2t)/(3+t) is -7/((3+t)^2)
What is the first derivative of G(t)=(1-2t)/(3+t) ?
The first derivative of G(t)=(1-2t)/(3+t) is -7/((3+t)^2)