What is the derivative of (3x^2-18x+25/(x^2-6x+8)) ?

The derivative of (3x^2-18x+25/(x^2-6x+8)) is (-2x+6)/((x^2-6x+8)^2)

What is the first derivative of (3x^2-18x+25/(x^2-6x+8)) ?

The first derivative of (3x^2-18x+25/(x^2-6x+8)) is (-2x+6)/((x^2-6x+8)^2)

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\frac{d}{d x} (\frac{3 x ^{2} - 18 x + 25}{x ^{2} - 6 x + 8})

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

Solution steps

\frac{d}{d x} (\frac{3 x ^{2} - 18 x + 25}{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} ( 3 x ^{2} - 18 x + 25 ) ( x ^{2} - 6 x + 8 ) - \frac{d}{d x} ( x ^{2} - 6 x + 8 ) ( 3 x ^{2} - 18 x + 25 )}{( x ^{2} - 6 x + 8 ) ^{2}}

\frac{d}{d x} (3 x^{2} - 18 x + 25) = 6 x - 18

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

= \frac{( 6 x - 18 ) ( x ^{2} - 6 x + 8 ) - ( 2 x - 6 ) ( 3 x ^{2} - 18 x + 25 )}{( x ^{2} - 6 x + 8 ) ^{2}}

Expand

(6 x - 18) (x^{2} - 6 x + 8) - (2 x - 6) (3 x^{2} - 18 x + 25) : - 2 x + 6

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

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

\frac{1 - e ^{- 2 s}}{6 s ^{2}}

x \to 0 lim (- cos (x) + 1)

\int \frac{5 x ^{2}}{x + 1} d x

y = x (1 - x)^{6}

What is the derivative of (3x^2-18x+25/(x^2-6x+8)) ?
The derivative of (3x^2-18x+25/(x^2-6x+8)) is (-2x+6)/((x^2-6x+8)^2)
What is the first derivative of (3x^2-18x+25/(x^2-6x+8)) ?
The first derivative of (3x^2-18x+25/(x^2-6x+8)) is (-2x+6)/((x^2-6x+8)^2)