What is the derivative of 15ln(x/(80)) ?

The derivative of 15ln(x/(80)) is (15)/x

What is the first derivative of 15ln(x/(80)) ?

The first derivative of 15ln(x/(80)) is (15)/x

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\frac{d}{d x} (15 ln (\frac{x}{80}))

\frac{15}{x}

Solution steps

\frac{d}{d x} (15 ln (\frac{x}{80}))

Take the constant out:

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

= 15 \frac{d}{d x} (ln (\frac{x}{80}))

Apply the chain rule:

\frac{1}{\frac{x}{80}} \frac{d}{d x} (\frac{x}{80})

= \frac{1}{\frac{x}{80}} \frac{d}{d x} (\frac{x}{80})

\frac{d}{d x} (\frac{x}{80}) = \frac{1}{80}

= 15 \cdot \frac{1}{\frac{x}{80}} \cdot \frac{1}{80}

Simplify

15 \cdot \frac{1}{\frac{x}{80}} \cdot \frac{1}{80} : \frac{15}{x}

= \frac{15}{x}

What is the derivative of 15ln(x/(80)) ?
The derivative of 15ln(x/(80)) is (15)/x
What is the first derivative of 15ln(x/(80)) ?
The first derivative of 15ln(x/(80)) is (15)/x