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Popular Calculus >

derivative of (1-6t)/(5+t)

Solution

derivative of

\frac{1 - 6 t}{5 + t}

Solution

- \frac{31}{( 5 + t ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{1 - 6 t}{5 + t})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d t} ( 1 - 6 t ) ( 5 + t ) - \frac{d}{d t} ( 5 + t ) ( 1 - 6 t )}{( 5 + t ) ^{2}}

\frac{d}{d t} (1 - 6 t) = - 6

\frac{d}{d t} (5 + t) = 1

= \frac{( - 6 ) ( 5 + t ) - 1 \cdot ( 1 - 6 t )}{( 5 + t ) ^{2}}

Simplify

\frac{( - 6 ) ( 5 + t ) - 1 \cdot ( 1 - 6 t )}{( 5 + t ) ^{2}} : - \frac{31}{( 5 + t ) ^{2}}

= - \frac{31}{( 5 + t ) ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (1-6t)/(5+t) ?
The derivative of (1-6t)/(5+t) is -(31)/((5+t)^2)
What is the first derivative of (1-6t)/(5+t) ?
The first derivative of (1-6t)/(5+t) is -(31)/((5+t)^2)