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

The derivative of ln(5x+1) is 5/(5x+1)

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

The first derivative of ln(5x+1) is 5/(5x+1)

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

\frac{5}{5 x + 1}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{5 x + 1} \cdot 5

Simplify

\frac{1}{5 x + 1} \cdot 5 : \frac{5}{5 x + 1}

= \frac{5}{5 x + 1}

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