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

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

= \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

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

Simplify

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

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

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

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

sin (x^{6}) + sin^{6} (x)

\frac{10 x}{( x + 7 )}

3 - x

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