What is the derivative of 12ln(x/(20)) ?

The derivative of 12ln(x/(20)) is (12)/x

What is the first derivative of 12ln(x/(20)) ?

The first derivative of 12ln(x/(20)) is (12)/x

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\frac{d}{d x} (12 ln (\frac{x}{20}))

\frac{12}{x}

Solution steps

\frac{d}{d x} (12 ln (\frac{x}{20}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 12 \frac{d}{d x} (ln (\frac{x}{20}))

Apply the chain rule:

\frac{1}{\frac{x}{20}} \frac{d}{d x} (\frac{x}{20})

= \frac{1}{\frac{x}{20}} \frac{d}{d x} (\frac{x}{20})

\frac{d}{d x} (\frac{x}{20}) = \frac{1}{20}

= 12 \cdot \frac{1}{\frac{x}{20}} \cdot \frac{1}{20}

Simplify

12 \cdot \frac{1}{\frac{x}{20}} \cdot \frac{1}{20} : \frac{12}{x}

= \frac{12}{x}

What is the derivative of 12ln(x/(20)) ?
The derivative of 12ln(x/(20)) is (12)/x
What is the first derivative of 12ln(x/(20)) ?
The first derivative of 12ln(x/(20)) is (12)/x