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

The derivative of t/((t-1)^2) is (-1-t)/((t-1)^3)

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

The first derivative of t/((t-1)^2) is (-1-t)/((t-1)^3)

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derivative of

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

\frac{- 1 - t}{( t - 1 ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{- 1 - t}{( t - 1 ) ^{3}}

(1, 1), (- 3, - 3)

y = x^{2} + x - 1.0 E - 13

\int \frac{1}{19 - x ^{2}} d x

3 t^{2} + 13 t

x \to 0 lim (\frac{( x ^{2} + 5 x )}{x})

What is the derivative of t/((t-1)^2) ?
The derivative of t/((t-1)^2) is (-1-t)/((t-1)^3)
What is the first derivative of t/((t-1)^2) ?
The first derivative of t/((t-1)^2) is (-1-t)/((t-1)^3)