What is the derivative of ln(1-(10/x)) ?

The derivative of ln(1-(10/x)) is (10)/(x(x-10))

What is the first derivative of ln(1-(10/x)) ?

The first derivative of ln(1-(10/x)) is (10)/(x(x-10))

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\frac{d}{d x} (ln (1 - \frac{10}{x}))

\frac{10}{x ( x - 10 )}

Solution steps

\frac{d}{d x} (ln (1 - \frac{10}{x}))

Apply the chain rule:

\frac{1}{1 - \frac{10}{x}} \frac{d}{d x} (1 - \frac{10}{x})

= \frac{1}{1 - \frac{10}{x}} \frac{d}{d x} (1 - \frac{10}{x})

\frac{d}{d x} (1 - \frac{10}{x}) = \frac{10}{x ^{2}}

= \frac{1}{1 - \frac{10}{x}} \cdot \frac{10}{x ^{2}}

Simplify

\frac{1}{1 - \frac{10}{x}} \cdot \frac{10}{x ^{2}} : \frac{10}{x ( x - 10 )}

= \frac{10}{x ( x - 10 )}

What is the derivative of ln(1-(10/x)) ?
The derivative of ln(1-(10/x)) is (10)/(x(x-10))
What is the first derivative of ln(1-(10/x)) ?
The first derivative of ln(1-(10/x)) is (10)/(x(x-10))