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

The derivative of (5x^2-9x+7/(3x+2)) is (15x^2+20x-39)/((3x+2)^2)

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

The first derivative of (5x^2-9x+7/(3x+2)) is (15x^2+20x-39)/((3x+2)^2)

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\frac{d}{d x} (\frac{5 x ^{2} - 9 x + 7}{3 x + 2})

\frac{15 x ^{2} + 20 x - 39}{( 3 x + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5 x ^{2} - 9 x + 7}{3 x + 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 5 x ^{2} - 9 x + 7 ) ( 3 x + 2 ) - \frac{d}{d x} ( 3 x + 2 ) ( 5 x ^{2} - 9 x + 7 )}{( 3 x + 2 ) ^{2}}

\frac{d}{d x} (5 x^{2} - 9 x + 7) = 10 x - 9

\frac{d}{d x} (3 x + 2) = 3

= \frac{( 10 x - 9 ) ( 3 x + 2 ) - 3 ( 5 x ^{2} - 9 x + 7 )}{( 3 x + 2 ) ^{2}}

Expand

(10 x - 9) (3 x + 2) - 3 (5 x^{2} - 9 x + 7) : 15 x^{2} + 20 x - 39

= \frac{15 x ^{2} + 20 x - 39}{( 3 x + 2 ) ^{2}}

\int (5 x^{2} + 7 x^{- 2}) d x

\frac{d y}{d x} = \frac{y ^{2}}{1 + x ^{2}}

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

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

y^{^{'}} = arctan (\frac{x}{2})

What is the derivative of (5x^2-9x+7/(3x+2)) ?
The derivative of (5x^2-9x+7/(3x+2)) is (15x^2+20x-39)/((3x+2)^2)
What is the first derivative of (5x^2-9x+7/(3x+2)) ?
The first derivative of (5x^2-9x+7/(3x+2)) is (15x^2+20x-39)/((3x+2)^2)