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Popular Calculus >

derivative of t/(t-1)

Solution

derivative of

\frac{t}{t - 1}

Solution

- \frac{1}{( t - 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d t}{d t} = 1

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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