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

The derivative of (t^2)/(t-2) is (t^2-4t)/((t-2)^2)

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

The first derivative of (t^2)/(t-2) is (t^2-4t)/((t-2)^2)

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derivative of

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

\frac{t ^{2} - 4 t}{( t - 2 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{t ^{2} - 4 t}{( t - 2 ) ^{2}}

What is the derivative of (t^2)/(t-2) ?
The derivative of (t^2)/(t-2) is (t^2-4t)/((t-2)^2)
What is the first derivative of (t^2)/(t-2) ?
The first derivative of (t^2)/(t-2) is (t^2-4t)/((t-2)^2)