What is the derivative of ln(f(x)) ?

The derivative of ln(f(x)) is 1/f

What is the first derivative of ln(f(x)) ?

The first derivative of ln(f(x)) is 1/f

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derivative of

ln (f (x))

\frac{1}{f}

Solution steps

\frac{d}{df} (ln (f x))

Treat

x

as a constant

Apply the chain rule:

\frac{1}{f x} \frac{d}{df} (f x)

= \frac{1}{f x} \frac{d}{df} (f x)

\frac{d}{df} (f x) = x

= \frac{1}{f x} x

Simplify

\frac{1}{f x} x : \frac{1}{f}

= \frac{1}{f}

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