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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{2 ( x - 1 )}{( - x + 1 ) ^{3}}

y^{^{'}} = x y

\int \frac{x}{10 - 0.8 x} d x

\int_{9}^{16} \frac{1}{6 - x} d x

\frac{d}{d x} (\frac{ln ( x ) - 10}{ln ( 10 )})

\int_{2}^{e^{4}} \frac{1}{x} d x

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