What is the derivative of (6(x-3^2)/(3x^2-9x-12)) ?

The derivative of (6(x-3^2)/(3x^2-9x-12)) is (2(x-3)(3x-17))/((x+1)^2(x-4)^2)

What is the first derivative of (6(x-3^2)/(3x^2-9x-12)) ?

The first derivative of (6(x-3^2)/(3x^2-9x-12)) is (2(x-3)(3x-17))/((x+1)^2(x-4)^2)

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\frac{d}{d x} (\frac{6 ( x - 3 ) ^{2}}{3 x ^{2} - 9 x - 12})

\frac{2 ( x - 3 ) ( 3 x - 17 )}{( x + 1 ) ^{2} ( x - 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6 ( x - 3 ) ^{2}}{3 x ^{2} - 9 x - 12})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (\frac{( x - 3 ) ^{2}}{3 x ^{2} - 9 x - 12})

Apply the Quotient Rule:

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

= 6 \cdot \frac{\frac{d}{d x} ( ( x - 3 ) ^{2} ) ( 3 x ^{2} - 9 x - 12 ) - \frac{d}{d x} ( 3 x ^{2} - 9 x - 12 ) ( x - 3 ) ^{2}}{( 3 x ^{2} - 9 x - 12 ) ^{2}}

\frac{d}{d x} ((x - 3)^{2}) = 2 (x - 3)

\frac{d}{d x} (3 x^{2} - 9 x - 12) = 6 x - 9

= 6 \cdot \frac{2 ( x - 3 ) ( 3 x ^{2} - 9 x - 12 ) - ( 6 x - 9 ) ( x - 3 ) ^{2}}{( 3 x ^{2} - 9 x - 12 ) ^{2}}

Simplify

6 \cdot \frac{2 ( x - 3 ) ( 3 x ^{2} - 9 x - 12 ) - ( 6 x - 9 ) ( x - 3 ) ^{2}}{( 3 x ^{2} - 9 x - 12 ) ^{2}} : \frac{2 ( x - 3 ) ( 3 x - 17 )}{( x + 1 ) ^{2} ( x - 4 ) ^{2}}

= \frac{2 ( x - 3 ) ( 3 x - 17 )}{( x + 1 ) ^{2} ( x - 4 ) ^{2}}

\frac{d}{d x} (3^{x^{2} + 1})

\int \frac{3}{x} + 1 d x

y = 4 (x - 1 x) 4, at x = 2

\frac{d}{d x} (\frac{1 + x}{2 + x})

\int 4 z + z 1 - z^{2} d z

What is the derivative of (6(x-3^2)/(3x^2-9x-12)) ?
The derivative of (6(x-3^2)/(3x^2-9x-12)) is (2(x-3)(3x-17))/((x+1)^2(x-4)^2)
What is the first derivative of (6(x-3^2)/(3x^2-9x-12)) ?
The first derivative of (6(x-3^2)/(3x^2-9x-12)) is (2(x-3)(3x-17))/((x+1)^2(x-4)^2)