What is the derivative of ((x^2-9x+20)/((x+2)(x-2))) ?

The derivative of ((x^2-9x+20)/((x+2)(x-2))) is (9x^2-48x+36)/((x+2)^2(x-2)^2)

What is the first derivative of ((x^2-9x+20)/((x+2)(x-2))) ?

The first derivative of ((x^2-9x+20)/((x+2)(x-2))) is (9x^2-48x+36)/((x+2)^2(x-2)^2)

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\frac{d}{d x} (\frac{( x ^{2} - 9 x + 20 )}{( x + 2 ) ( x - 2 )})

\frac{9 x ^{2} - 48 x + 36}{( x + 2 ) ^{2} ( x - 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{( x ^{2} - 9 x + 20 )}{( 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} - 9 x + 20 ) ( x + 2 ) ( x - 2 ) - \frac{d}{d x} ( ( x + 2 ) ( x - 2 ) ) ( x ^{2} - 9 x + 20 )}{( ( x + 2 ) ( x - 2 ) ) ^{2}}

\frac{d}{d x} (x^{2} - 9 x + 20) = 2 x - 9

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

= \frac{( 2 x - 9 ) ( x + 2 ) ( x - 2 ) - 2 x ( x ^{2} - 9 x + 20 )}{( ( x + 2 ) ( x - 2 ) ) ^{2}}

Simplify

\frac{( 2 x - 9 ) ( x + 2 ) ( x - 2 ) - 2 x ( x ^{2} - 9 x + 20 )}{( ( x + 2 ) ( x - 2 ) ) ^{2}} : \frac{9 x ^{2} - 48 x + 36}{( x + 2 ) ^{2} ( x - 2 ) ^{2}}

= \frac{9 x ^{2} - 48 x + 36}{( x + 2 ) ^{2} ( x - 2 ) ^{2}}

\int_{1}^{4} \frac{6}{x} d x

\int \frac{3 x - 2}{x ^{5}} d x

\frac{d}{d x} (2 cos (x) - x sin (x))

n = 0 \sum \infty (\frac{6}{7})^{n}

\frac{d y}{d x} + 12 y = 4

What is the derivative of ((x^2-9x+20)/((x+2)(x-2))) ?
The derivative of ((x^2-9x+20)/((x+2)(x-2))) is (9x^2-48x+36)/((x+2)^2(x-2)^2)
What is the first derivative of ((x^2-9x+20)/((x+2)(x-2))) ?
The first derivative of ((x^2-9x+20)/((x+2)(x-2))) is (9x^2-48x+36)/((x+2)^2(x-2)^2)