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Popular >

derivative of ln(1-3/x)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (1 - \frac{3}{x}) = \frac{3}{x ^{2}}

= \frac{1}{1 - \frac{3}{x}} \cdot \frac{3}{x ^{2}}

Simplify

\frac{1}{1 - \frac{3}{x}} \cdot \frac{3}{x ^{2}} : \frac{3}{x ( x - 3 )}

= \frac{3}{x ( x - 3 )}

Graph

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\int \frac{2}{x ^{3}} d x

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Frequently Asked Questions (FAQ)

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