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

The derivative of f(x)=((x+1)(3x-7))/(3x+1) is (9x^2+6x+17)/((3x+1)^2)

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

The first derivative of f(x)=((x+1)(3x-7))/(3x+1) is (9x^2+6x+17)/((3x+1)^2)

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derivative of

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

\frac{9 x ^{2} + 6 x + 17}{( 3 x + 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} ((x + 1) (3 x - 7)) = 6 x - 4

\frac{d}{d x} (3 x + 1) = 3

= \frac{( 6 x - 4 ) ( 3 x + 1 ) - 3 ( x + 1 ) ( 3 x - 7 )}{( 3 x + 1 ) ^{2}}

Expand

(6 x - 4) (3 x + 1) - 3 (x + 1) (3 x - 7) : 9 x^{2} + 6 x + 17

= \frac{9 x ^{2} + 6 x + 17}{( 3 x + 1 ) ^{2}}

\int x^{4} 9 + x^{5} d x

\int 11 x^{\frac{4}{7}} + 4 x^{- \frac{6}{7}} d x

\frac{d}{d x} ((ln (x))^{s i n h (x)})

\int 9 cos (x) sin (x) d x

\frac{d}{d x} (\frac{x ^{2}}{7})

What is the derivative of f(x)=((x+1)(3x-7))/(3x+1) ?
The derivative of f(x)=((x+1)(3x-7))/(3x+1) is (9x^2+6x+17)/((3x+1)^2)
What is the first derivative of f(x)=((x+1)(3x-7))/(3x+1) ?
The first derivative of f(x)=((x+1)(3x-7))/(3x+1) is (9x^2+6x+17)/((3x+1)^2)