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Popular >

derivative of ln(K/x)

Solution

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

Solution

\frac{x \frac{d K}{d x} - K}{x K}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{\frac{K}{x}} \cdot \frac{x \frac{d K}{d x} - K}{x ^{2}} : \frac{x \frac{d K}{d x} - K}{x K}

= \frac{x \frac{d K}{d x} - K}{x K}

Popular Examples

integral of e^{-15x}

\int e^{- 15 x} d x

inverse oflaplace 1/(s^2+7)inverse laplace

\frac{1}{s ^{2} + 7}

integral of (sqrt(n)+3)^3

\int (n + 3)^{3} d n

integral of ln^2(x-9)

\int ln^{2} (x - 9) d x

simplify ln(x^2)-1/(x^2)-5 simplify

ln (x^{2}) - \frac{1}{x ^{2}} - 5

Frequently Asked Questions (FAQ)

What is the derivative of ln(K/x) ?
The derivative of ln(K/x) is (x\frac{dK)/(dx)-K}{xK}
What is the first derivative of ln(K/x) ?
The first derivative of ln(K/x) is (x\frac{dK)/(dx)-K}{xK}