What is the derivative of (x^2-x-2)/(x^2-6x+9) ?

The derivative of (x^2-x-2)/(x^2-6x+9) is -(5x-7)/((x-3)^3)

What is the first derivative of (x^2-x-2)/(x^2-6x+9) ?

The first derivative of (x^2-x-2)/(x^2-6x+9) is -(5x-7)/((x-3)^3)

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derivative of

\frac{x ^{2} - x - 2}{x ^{2} - 6 x + 9}

- \frac{5 x - 7}{( x - 3 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} - x - 2}{x ^{2} - 6 x + 9})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} - x - 2 ) ( x ^{2} - 6 x + 9 ) - \frac{d}{d x} ( x ^{2} - 6 x + 9 ) ( x ^{2} - x - 2 )}{( x ^{2} - 6 x + 9 ) ^{2}}

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

\frac{d}{d x} (x^{2} - 6 x + 9) = 2 x - 6

= \frac{( 2 x - 1 ) ( x ^{2} - 6 x + 9 ) - ( 2 x - 6 ) ( x ^{2} - x - 2 )}{( x ^{2} - 6 x + 9 ) ^{2}}

Simplify

\frac{( 2 x - 1 ) ( x ^{2} - 6 x + 9 ) - ( 2 x - 6 ) ( x ^{2} - x - 2 )}{( x ^{2} - 6 x + 9 ) ^{2}} : - \frac{5 x - 7}{( x - 3 ) ^{3}}

= - \frac{5 x - 7}{( x - 3 ) ^{3}}

\frac{d}{d x} (arctan (5^{x}))

\int \frac{1 - x}{x} d x

x \to 6 + lim (ln (x - 6))

y = sin (x) + x cos (x)

\int_{0}^{5} \frac{1}{x ^{\frac{19}{18}}} d x

What is the derivative of (x^2-x-2)/(x^2-6x+9) ?
The derivative of (x^2-x-2)/(x^2-6x+9) is -(5x-7)/((x-3)^3)
What is the first derivative of (x^2-x-2)/(x^2-6x+9) ?
The first derivative of (x^2-x-2)/(x^2-6x+9) is -(5x-7)/((x-3)^3)