What is the derivative of ln(5/x) ?

The derivative of ln(5/x) is -1/x

What is the first derivative of ln(5/x) ?

The first derivative of ln(5/x) is -1/x

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\frac{d}{d x} (ln (\frac{5}{x}))

- \frac{1}{x}

Solution steps

\frac{d}{d x} (ln (\frac{5}{x}))

Apply the chain rule:

\frac{1}{\frac{5}{x}} \frac{d}{d x} (\frac{5}{x})

= \frac{1}{\frac{5}{x}} \frac{d}{d x} (\frac{5}{x})

\frac{d}{d x} (\frac{5}{x}) = - \frac{5}{x ^{2}}

= \frac{1}{\frac{5}{x}} (- \frac{5}{x ^{2}})

Simplify

\frac{1}{\frac{5}{x}} (- \frac{5}{x ^{2}}) : - \frac{1}{x}

= - \frac{1}{x}

y^{^{''}} + 2 y^{^{'}} - 3 y = 2 x - 17

\frac{1}{cos ( x )}

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

\int_{0}^{2} 4 x^{3} d x

3 x^{4} (4 - x)^{3}

What is the derivative of ln(5/x) ?
The derivative of ln(5/x) is -1/x
What is the first derivative of ln(5/x) ?
The first derivative of ln(5/x) is -1/x