What is the derivative of g(x)=(2x+2)/(x^2+2) ?

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

What is the first derivative of g(x)=(2x+2)/(x^2+2) ?

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

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derivative of

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

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

Solution steps

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

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

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

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

Expand

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

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

n = 0 \sum \infty n

(x, y) \to (- 6, 5) lim (\frac{x ^{2} cos ( π y )}{e ^{x + y}})

\frac{d ^{2}}{d x ^{2}} (cos (π x))

\int \frac{8}{x ^{2} + 9} d x

\frac{1}{4 s + 7}

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