What is the derivative of ln(9/x) ?

The derivative of ln(9/x) is -1/x

What is the first derivative of ln(9/x) ?

The first derivative of ln(9/x) is -1/x

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derivative of

ln (\frac{9}{x})

- \frac{1}{x}

Solution steps

\frac{d}{d x} (ln (\frac{9}{x}))

Apply the chain rule:

\frac{1}{\frac{9}{x}} \frac{d}{d x} (\frac{9}{x})

= \frac{1}{\frac{9}{x}} \frac{d}{d x} (\frac{9}{x})

\frac{d}{d x} (\frac{9}{x}) = - \frac{9}{x ^{2}}

= \frac{1}{\frac{9}{x}} (- \frac{9}{x ^{2}})

Simplify

\frac{1}{\frac{9}{x}} (- \frac{9}{x ^{2}}) : - \frac{1}{x}

= - \frac{1}{x}

e^{x} - 2

\frac{w \cdot v t x ^{2} + x}{x ^{2} + 2 x + 7}

\frac{d}{d r} (3.14 r^{3})

y = 5 x^{2} - 6 x + 12

(9 x^{8} - 8 x^{9}) (\frac{x + 1}{x})

What is the derivative of ln(9/x) ?
The derivative of ln(9/x) is -1/x
What is the first derivative of ln(9/x) ?
The first derivative of ln(9/x) is -1/x