505Log

Derivative of Natural Logarithms

math \dfrac {d}{dx} \left( \log_e ax \right) = \dfrac {a}{ax} = \dfrac {1}{x} math

Example

math \dfrac {d}{dx} \left( \log_e 3x \right) = \dfrac {1}{x} math

**Chain Rule Version** math \dfrac {d}{dx} \Big( \log_e g(x) \Big) = \dfrac {g'(x)}{g(x)} math

Example

math \dfrac {d}{dx} \Big( \log_e \left(x^3+4x^2 \right) \Big) = \dfrac {3x^2+8x}{x^3+4x^2} math

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