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Popular >

derivative of f(t)= t/(t^2-2)

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

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

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

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Frequently Asked Questions (FAQ)

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