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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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