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Popular >

derivative of ln(1-1/x)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial x)(3y^2+20x^2y^3)

\frac{\partial}{\partial x} (3 y^{2} + 20 x^{2} y^{3})

laplacetransform cos^2(pit)laplace transform

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x^{2} y^{^{'}} + x y = y^{2}

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x \to - 1 lim ((x + 1) \cdot ln (x + 1))

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\frac{2}{s + 1} + 32 \cdot \frac{s}{s ^{2} + 9}

Frequently Asked Questions (FAQ)

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