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

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

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

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

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derivative of

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

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

Solution steps

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

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

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

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

Expand

2 (x - 1) (x^{2} + 1) - 2 x (x - 1)^{2} : 2 x^{2} - 2

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

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

h \to 0 lim (3 h + 18)

f (x) = \frac{1}{2} x ln (x^{2}), (- 1, 0)

\int cos (θ) + sin (θ) d θ

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