What is the derivative of f(x)=(7x^2-6x+1)/(3x+2) ?

The derivative of f(x)=(7x^2-6x+1)/(3x+2) is (21x^2+28x-15)/((3x+2)^2)

What is the first derivative of f(x)=(7x^2-6x+1)/(3x+2) ?

The first derivative of f(x)=(7x^2-6x+1)/(3x+2) is (21x^2+28x-15)/((3x+2)^2)

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derivative of

f (x) = \frac{7 x ^{2} - 6 x + 1}{3 x + 2}

\frac{21 x ^{2} + 28 x - 15}{( 3 x + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{7 x ^{2} - 6 x + 1}{3 x + 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 7 x ^{2} - 6 x + 1 ) ( 3 x + 2 ) - \frac{d}{d x} ( 3 x + 2 ) ( 7 x ^{2} - 6 x + 1 )}{( 3 x + 2 ) ^{2}}

\frac{d}{d x} (7 x^{2} - 6 x + 1) = 14 x - 6

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

= \frac{( 14 x - 6 ) ( 3 x + 2 ) - 3 ( 7 x ^{2} - 6 x + 1 )}{( 3 x + 2 ) ^{2}}

Expand

(14 x - 6) (3 x + 2) - 3 (7 x^{2} - 6 x + 1) : 21 x^{2} + 28 x - 15

= \frac{21 x ^{2} + 28 x - 15}{( 3 x + 2 ) ^{2}}

\frac{d ^{2}}{d x ^{2}} (3 + 5 x + 2 x^{2} + 0.4 x^{3})

y^{^{''}} + 9 y = 2 sin (3 x)

y^{^{'}} = 4 x y

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

3 e^{x} + \frac{8}{3 x}

What is the derivative of f(x)=(7x^2-6x+1)/(3x+2) ?
The derivative of f(x)=(7x^2-6x+1)/(3x+2) is (21x^2+28x-15)/((3x+2)^2)
What is the first derivative of f(x)=(7x^2-6x+1)/(3x+2) ?
The first derivative of f(x)=(7x^2-6x+1)/(3x+2) is (21x^2+28x-15)/((3x+2)^2)