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

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

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

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

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derivative of

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

\frac{- 2 - t}{( t - 2 ) ^{3}}

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 - 2)

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

Simplify

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

= \frac{- 2 - t}{( t - 2 ) ^{3}}

5 y^{^{''}} - 4 y^{^{'}} = 0

\int \frac{2}{x x ^{2} + 1} d x

\frac{e ^{- s}}{s \cdot ( s + 5 ) ^{2}}

\frac{d}{d x} (\frac{ln ( 3 x )}{3 x})

\int \frac{16}{( x + 2 ) ( x ^{2} - 4 )} d x

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