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

The derivative of ((x-1^2)/(x^2+2)) is (2x^2+2x-4)/((x^2+2)^2)

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

The first derivative of ((x-1^2)/(x^2+2)) is (2x^2+2x-4)/((x^2+2)^2)

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

\frac{2 x ^{2} + 2 x - 4}{( x ^{2} + 2 ) ^{2}}

Solution steps

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

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

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

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

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

Expand

2 (x - 1) (x^{2} + 2) - 2 x (x - 1)^{2} : 2 x^{2} + 2 x - 4

= \frac{2 x ^{2} + 2 x - 4}{( x ^{2} + 2 ) ^{2}}

f (x) = (x - 1) (x^{2} - 8 x + 7)

f (x) = \frac{- cos ( x )}{4 x ^{2} + 2 x - 3}

\frac{1}{( s - 5 ) ^{3}}

\frac{\partial}{\partial x} (56 e^{8 x} y)

\int_{0}^{\frac{π}{2}} (sin (2 x)) d x

What is the derivative of ((x-1^2)/(x^2+2)) ?
The derivative of ((x-1^2)/(x^2+2)) is (2x^2+2x-4)/((x^2+2)^2)
What is the first derivative of ((x-1^2)/(x^2+2)) ?
The first derivative of ((x-1^2)/(x^2+2)) is (2x^2+2x-4)/((x^2+2)^2)