What is the derivative of (x^2-4x+20/(x^2+6x+8)) ?

The derivative of (x^2-4x+20/(x^2+6x+8)) is (10x^2-24x-152)/((x^2+6x+8)^2)

What is the first derivative of (x^2-4x+20/(x^2+6x+8)) ?

The first derivative of (x^2-4x+20/(x^2+6x+8)) is (10x^2-24x-152)/((x^2+6x+8)^2)

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\frac{d}{d x} (\frac{x ^{2} - 4 x + 20}{x ^{2} + 6 x + 8})

\frac{10 x ^{2} - 24 x - 152}{( x ^{2} + 6 x + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} - 4 x + 20}{x ^{2} + 6 x + 8})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} - 4 x + 20 ) ( x ^{2} + 6 x + 8 ) - \frac{d}{d x} ( x ^{2} + 6 x + 8 ) ( x ^{2} - 4 x + 20 )}{( x ^{2} + 6 x + 8 ) ^{2}}

\frac{d}{d x} (x^{2} - 4 x + 20) = 2 x - 4

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

= \frac{( 2 x - 4 ) ( x ^{2} + 6 x + 8 ) - ( 2 x + 6 ) ( x ^{2} - 4 x + 20 )}{( x ^{2} + 6 x + 8 ) ^{2}}

Expand

(2 x - 4) (x^{2} + 6 x + 8) - (2 x + 6) (x^{2} - 4 x + 20) : 10 x^{2} - 24 x - 152

= \frac{10 x ^{2} - 24 x - 152}{( x ^{2} + 6 x + 8 ) ^{2}}

What is the derivative of (x^2-4x+20/(x^2+6x+8)) ?
The derivative of (x^2-4x+20/(x^2+6x+8)) is (10x^2-24x-152)/((x^2+6x+8)^2)
What is the first derivative of (x^2-4x+20/(x^2+6x+8)) ?
The first derivative of (x^2-4x+20/(x^2+6x+8)) is (10x^2-24x-152)/((x^2+6x+8)^2)