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

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

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

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

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derivative of

ln (\frac{x}{y})

\frac{1}{x}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x}

\int sin (2 x) sin (6 x) d x

\frac{d}{d x} (3 2 - x)

\int_{3}^{\infty} \frac{2}{x ^{2} - 1} d x

ln (1 + z)

\frac{\partial}{\partial x} (42 y^{6} x^{5} - 30 y^{5} x^{4})

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