What is the derivative of 1/(3x+6) ?

The derivative of 1/(3x+6) is -1/(3(x+2)^2)

What is the first derivative of 1/(3x+6) ?

The first derivative of 1/(3x+6) is -1/(3(x+2)^2)

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\frac{d}{d x} (\frac{1}{3 x + 6})

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

Solution steps

\frac{d}{d x} (\frac{1}{3 x + 6})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x + 6) = 3

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

Simplify

- \frac{1}{( 3 x + 6 ) ^{2}} \cdot 3 : - \frac{1}{3 ( x + 2 ) ^{2}}

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

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

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

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

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

\int (4 + x) d x

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