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Popular >

derivative of ln(1-2/x)

Solution

\frac{d}{d x} (ln (1 - \frac{2}{x}))

Solution

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

Solution steps

\frac{d}{d x} (ln (1 - \frac{2}{x}))

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2}{x ( x - 2 )}

Graph

Popular Examples

integral of (25-0.2x)

\int (25 - 0.2 x) d x

derivative of f(x)= 1/(\sqrt[9]{x)}derivative of

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

(\partial)/(\partial x)(t^4e^{-x})

\frac{\partial}{\partial x} (t^{4} e^{- x})

integral of (2/(sqrt(x))-3xsqrt(x)+2)

\int (\frac{2}{x} - 3 x x + 2) d x

tangent of y=-x^3+2x^2+1,\at x=-1 tangent of

y = - x^{3} + 2 x^{2} + 1, at x = - 1

Frequently Asked Questions (FAQ)

What is the derivative of ln(1-2/x) ?
The derivative of ln(1-2/x) is 2/(x(x-2))
What is the first derivative of ln(1-2/x) ?
The first derivative of ln(1-2/x) is 2/(x(x-2))