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

The derivative of ((x+2(2x+4))/(-x^2-x-2)) is (6x^2+8x-8)/((-x^2-x-2)^2)

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

The first derivative of ((x+2(2x+4))/(-x^2-x-2)) is (6x^2+8x-8)/((-x^2-x-2)^2)

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

\frac{6 x ^{2} + 8 x - 8}{( - x ^{2} - x - 2 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} ((x + 2) (2 x + 4)) = 4 x + 8

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

= \frac{( 4 x + 8 ) ( - x ^{2} - x - 2 ) - ( - 2 x - 1 ) ( x + 2 ) ( 2 x + 4 )}{( - x ^{2} - x - 2 ) ^{2}}

Expand

(4 x + 8) (- x^{2} - x - 2) - (- 2 x - 1) (x + 2) (2 x + 4) : 6 x^{2} + 8 x - 8

= \frac{6 x ^{2} + 8 x - 8}{( - x ^{2} - x - 2 ) ^{2}}

r^{2} - 15 x^{2}

lo g_{7} (x e^{x})

\frac{d}{d x} (\frac{7 x}{x ^{2} + 5})

\int e^{x} sin (2 x) d x

\int \frac{x ( x - 2 ) ^{2}}{x ^{4} + 1} d x

What is the derivative of ((x+2(2x+4))/(-x^2-x-2)) ?
The derivative of ((x+2(2x+4))/(-x^2-x-2)) is (6x^2+8x-8)/((-x^2-x-2)^2)
What is the first derivative of ((x+2(2x+4))/(-x^2-x-2)) ?
The first derivative of ((x+2(2x+4))/(-x^2-x-2)) is (6x^2+8x-8)/((-x^2-x-2)^2)