What is the derivative of ln(x/3) ?

The derivative of ln(x/3) is 1/x

What is the first derivative of ln(x/3) ?

The first derivative of ln(x/3) is 1/x

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\frac{d}{d x} (ln (\frac{x}{3}))

\frac{1}{x}

Solution steps

\frac{d}{d x} (ln (\frac{x}{3}))

Apply the chain rule:

\frac{1}{\frac{x}{3}} \frac{d}{d x} (\frac{x}{3})

= \frac{1}{\frac{x}{3}} \frac{d}{d x} (\frac{x}{3})

\frac{d}{d x} (\frac{x}{3}) = \frac{1}{3}

= \frac{1}{\frac{x}{3}} \cdot \frac{1}{3}

Simplify

\frac{1}{\frac{x}{3}} \cdot \frac{1}{3} : \frac{1}{x}

= \frac{1}{x}

\frac{\partial}{\partial z} (x^{2} y e^{\frac{y}{z}})

\int sin (x) sin (4 x) d x

\frac{d}{d x} (e^{x + 7})

\frac{\partial}{\partial x} (- \frac{e ^{\frac{y}{x}} y}{x ^{2}} + e^{- x} y)

n = 0 \sum \infty e^{\frac{1}{n}}

What is the derivative of ln(x/3) ?
The derivative of ln(x/3) is 1/x
What is the first derivative of ln(x/3) ?
The first derivative of ln(x/3) is 1/x