What is the derivative of f(x)= x/((x-1)^2) ?

The derivative of f(x)= x/((x-1)^2) is (-1-x)/((x-1)^3)

What is the first derivative of f(x)= x/((x-1)^2) ?

The first derivative of f(x)= x/((x-1)^2) is (-1-x)/((x-1)^3)

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derivative of

f (x) = \frac{x}{( x - 1 ) ^{2}}

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

\frac{d}{d t} (ln (2 t))

\int_{0}^{1} \frac{1}{x ^{3}} d x

\int \frac{9 t - 5}{t + 1} d t

x \to 0 lim (\frac{x - 32}{x - 4})

\int 7 x - 14 d x

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