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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (x^{3} + x + 2)

\int x - 2 cos (x) d x

\frac{d}{d x} (- \frac{x ^{3}}{y ^{3}})

\frac{d}{d x} (\frac{27}{x})

12 x

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