What is the derivative of (1/(3x+1)^4) ?

The derivative of (1/(3x+1)^4) is -(12)/((3x+1)^5)

What is the first derivative of (1/(3x+1)^4) ?

The first derivative of (1/(3x+1)^4) is -(12)/((3x+1)^5)

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\frac{d}{d x} ((\frac{1}{3 x + 1})^{4})

- \frac{12}{( 3 x + 1 ) ^{5}}

Solution steps

\frac{d}{d x} ((\frac{1}{3 x + 1})^{4})

Apply the chain rule:

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

= 4 (\frac{1}{3 x + 1})^{3} \frac{d}{d x} (\frac{1}{3 x + 1})

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

= 4 (\frac{1}{3 x + 1})^{3} (- \frac{3}{( 3 x + 1 ) ^{2}})

Simplify

4 (\frac{1}{3 x + 1})^{3} (- \frac{3}{( 3 x + 1 ) ^{2}}) : - \frac{12}{( 3 x + 1 ) ^{5}}

= - \frac{12}{( 3 x + 1 ) ^{5}}

What is the derivative of (1/(3x+1)^4) ?
The derivative of (1/(3x+1)^4) is -(12)/((3x+1)^5)
What is the first derivative of (1/(3x+1)^4) ?
The first derivative of (1/(3x+1)^4) is -(12)/((3x+1)^5)