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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derivative of

\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}}

\frac{\partial}{\partial x} (y x^{3} - x y^{2} + x y + 13 y)

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

f (x) = 9 e^{x}, at x = 7

\int_{1}^{12} \frac{1}{x - 7} d x

\frac{\partial}{\partial y} (x^{2} + 6 x y + 4 y^{2})

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)