What is the derivative of ln(5t) ?

The derivative of ln(5t) is 1/t

What is the first derivative of ln(5t) ?

The first derivative of ln(5t) is 1/t

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derivative of

ln (5 t)

\frac{1}{t}

Solution steps

\frac{d}{d t} (ln (5 t))

Apply the chain rule:

\frac{1}{5 t} \frac{d}{d t} (5 t)

= \frac{1}{5 t} \frac{d}{d t} (5 t)

\frac{d}{d t} (5 t) = 5

= \frac{1}{5 t} \cdot 5

Simplify

\frac{1}{5 t} \cdot 5 : \frac{1}{t}

= \frac{1}{t}

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