What is the derivative of b*ln(x/a) ?

The derivative of b*ln(x/a) is b/x

What is the first derivative of b*ln(x/a) ?

The first derivative of b*ln(x/a) is b/x

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derivative of

b \cdot ln (\frac{x}{a})

\frac{b}{x}

Solution steps

\frac{d}{d x} (b ln (\frac{x}{a}))

Take the constant out:

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

= b \frac{d}{d x} (ln (\frac{x}{a}))

Apply the chain rule:

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

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

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

= b \frac{1}{\frac{x}{a}} \cdot \frac{1}{a}

Simplify

b \frac{1}{\frac{x}{a}} \cdot \frac{1}{a} : \frac{b}{x}

= \frac{b}{x}

What is the derivative of b*ln(x/a) ?
The derivative of b*ln(x/a) is b/x
What is the first derivative of b*ln(x/a) ?
The first derivative of b*ln(x/a) is b/x