Section 5.8

Logarithmic differentiation

\frac{d}{dx}[\ln|f(x)|]=\frac{f'(x)}{f(x)},\qquad f(x)\neq0

Useful for variable powers and products/quotients.

viz

y=f(x)^{g(x)} \Rightarrow \ln y=g(x)\ln f(x),\qquad f(x)>0

First step to differentiate $f^g$ with variable exponent (requires $f(x)>0$ where $\ln$ is applied).

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Section 5.8

\frac{d}{dx}[\ln|f(x)|]=\frac{f'(x)}{f(x)},\qquad f(x)\neq0

Useful for variable powers and products/quotients.

viz

y=f(x)^{g(x)} \Rightarrow \ln y=g(x)\ln f(x),\qquad f(x)>0

First step to differentiate $f^g$ with variable exponent (requires $f(x)>0$ where $\ln$ is applied).