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

The derivative of-3/(3x+2) is 9/((3x+2)^2)

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

The first derivative of-3/(3x+2) is 9/((3x+2)^2)

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

- 3 (- \frac{1}{( 3 x + 2 ) ^{2}} \cdot 3) : \frac{9}{( 3 x + 2 ) ^{2}}

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

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