What is the derivative of 1/(5x+1) ?

The derivative of 1/(5x+1) is -5/((5x+1)^2)

What is the first derivative of 1/(5x+1) ?

The first derivative of 1/(5x+1) is -5/((5x+1)^2)

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\frac{d}{d x} (\frac{1}{5 x + 1})

- \frac{5}{( 5 x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{5 x + 1})

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{1}{( 5 x + 1 ) ^{2}} \frac{d}{d x} (5 x + 1)

= - \frac{1}{( 5 x + 1 ) ^{2}} \frac{d}{d x} (5 x + 1)

\frac{d}{d x} (5 x + 1) = 5

= - \frac{1}{( 5 x + 1 ) ^{2}} \cdot 5

Simplify

- \frac{1}{( 5 x + 1 ) ^{2}} \cdot 5 : - \frac{5}{( 5 x + 1 ) ^{2}}

= - \frac{5}{( 5 x + 1 ) ^{2}}

What is the derivative of 1/(5x+1) ?
The derivative of 1/(5x+1) is -5/((5x+1)^2)
What is the first derivative of 1/(5x+1) ?
The first derivative of 1/(5x+1) is -5/((5x+1)^2)