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Logarithmic Differentiation for Powers
For:
$$y=u(x)^{v(x)}$$
taking logarithms gives:
$$\ln y=v(x)\ln u(x)$$
Differentiating:
$$\frac{y'}{y}=v'(x)\ln u(x)+v(x)\frac{u'(x)}{u(x)}$$
Usage
- Used to differentiate variable-base and variable-exponent functions.
