What is the derivative of (3x^2-9x+13)/(3x+4) ?

The derivative of (3x^2-9x+13)/(3x+4) is (9x^2+24x-75)/((3x+4)^2)

What is the first derivative of (3x^2-9x+13)/(3x+4) ?

The first derivative of (3x^2-9x+13)/(3x+4) is (9x^2+24x-75)/((3x+4)^2)

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derivative of

\frac{3 x ^{2} - 9 x + 13}{3 x + 4}

\frac{9 x ^{2} + 24 x - 75}{( 3 x + 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x ^{2} - 9 x + 13}{3 x + 4})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x ^{2} - 9 x + 13 ) ( 3 x + 4 ) - \frac{d}{d x} ( 3 x + 4 ) ( 3 x ^{2} - 9 x + 13 )}{( 3 x + 4 ) ^{2}}

\frac{d}{d x} (3 x^{2} - 9 x + 13) = 6 x - 9

\frac{d}{d x} (3 x + 4) = 3

= \frac{( 6 x - 9 ) ( 3 x + 4 ) - 3 ( 3 x ^{2} - 9 x + 13 )}{( 3 x + 4 ) ^{2}}

Expand

(6 x - 9) (3 x + 4) - 3 (3 x^{2} - 9 x + 13) : 9 x^{2} + 24 x - 75

= \frac{9 x ^{2} + 24 x - 75}{( 3 x + 4 ) ^{2}}

\int - x^{2} + 4 x - 3 d x

\frac{d}{d x} (9 tan (x))

\frac{\partial}{\partial x} (\frac{10 x}{1 + x ^{2} - y})

\frac{\partial}{\partial y} (\frac{y}{2})

f (x) = 3 x^{2} - 1

What is the derivative of (3x^2-9x+13)/(3x+4) ?
The derivative of (3x^2-9x+13)/(3x+4) is (9x^2+24x-75)/((3x+4)^2)
What is the first derivative of (3x^2-9x+13)/(3x+4) ?
The first derivative of (3x^2-9x+13)/(3x+4) is (9x^2+24x-75)/((3x+4)^2)