What is the derivative of t/((t-6)^2) ?

The derivative of t/((t-6)^2) is (-6-t)/((t-6)^3)

What is the first derivative of t/((t-6)^2) ?

The first derivative of t/((t-6)^2) is (-6-t)/((t-6)^3)

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derivative of

\frac{t}{( t - 6 ) ^{2}}

\frac{- 6 - t}{( t - 6 ) ^{3}}

Solution steps

\frac{d}{d t} (\frac{t}{( t - 6 ) ^{2}})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot ( t - 6 ) ^{2} - 2 ( t - 6 ) t}{( ( t - 6 ) ^{2} ) ^{2}} : \frac{- 6 - t}{( t - 6 ) ^{3}}

= \frac{- 6 - t}{( t - 6 ) ^{3}}

What is the derivative of t/((t-6)^2) ?
The derivative of t/((t-6)^2) is (-6-t)/((t-6)^3)
What is the first derivative of t/((t-6)^2) ?
The first derivative of t/((t-6)^2) is (-6-t)/((t-6)^3)