What is the derivative of (x+1/(3x+2)) ?

The derivative of (x+1/(3x+2)) is -1/((3x+2)^2)

What is the first derivative of (x+1/(3x+2)) ?

The first derivative of (x+1/(3x+2)) is -1/((3x+2)^2)

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

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

Solution steps

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

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

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

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

Simplify

\frac{1 \cdot ( 3 x + 2 ) - 3 ( x + 1 )}{( 3 x + 2 ) ^{2}} : - \frac{1}{( 3 x + 2 ) ^{2}}

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

What is the derivative of (x+1/(3x+2)) ?
The derivative of (x+1/(3x+2)) is -1/((3x+2)^2)
What is the first derivative of (x+1/(3x+2)) ?
The first derivative of (x+1/(3x+2)) is -1/((3x+2)^2)