What is the derivative of (4x^2-7x+6/(3x+5)) ?

The derivative of (4x^2-7x+6/(3x+5)) is (12x^2+40x-53)/((3x+5)^2)

What is the first derivative of (4x^2-7x+6/(3x+5)) ?

The first derivative of (4x^2-7x+6/(3x+5)) is (12x^2+40x-53)/((3x+5)^2)

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\frac{d}{d x} (\frac{4 x ^{2} - 7 x + 6}{3 x + 5})

\frac{12 x ^{2} + 40 x - 53}{( 3 x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x ^{2} - 7 x + 6}{3 x + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x ^{2} - 7 x + 6 ) ( 3 x + 5 ) - \frac{d}{d x} ( 3 x + 5 ) ( 4 x ^{2} - 7 x + 6 )}{( 3 x + 5 ) ^{2}}

\frac{d}{d x} (4 x^{2} - 7 x + 6) = 8 x - 7

\frac{d}{d x} (3 x + 5) = 3

= \frac{( 8 x - 7 ) ( 3 x + 5 ) - 3 ( 4 x ^{2} - 7 x + 6 )}{( 3 x + 5 ) ^{2}}

Expand

(8 x - 7) (3 x + 5) - 3 (4 x^{2} - 7 x + 6) : 12 x^{2} + 40 x - 53

= \frac{12 x ^{2} + 40 x - 53}{( 3 x + 5 ) ^{2}}

x y^{^{'}} = y + x^{2} sin (x)

\frac{d}{d x} (e^{x} x^{2} + 2 x e^{x})

\int \frac{1}{529 + x ^{2}} d x

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

11 e^{x}

What is the derivative of (4x^2-7x+6/(3x+5)) ?
The derivative of (4x^2-7x+6/(3x+5)) is (12x^2+40x-53)/((3x+5)^2)
What is the first derivative of (4x^2-7x+6/(3x+5)) ?
The first derivative of (4x^2-7x+6/(3x+5)) is (12x^2+40x-53)/((3x+5)^2)