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Logarithmic Form of a Variable Power
If:
$$y=u(x)^{v(x)}$$
then:
$$\ln y=v(x)\ln u(x)$$
Hence:
$$y=e^{v(x)\ln u(x)}$$
Usage
- General method for differentiating or evaluating variable-base, variable-exponent expressions.
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Logarithmic Form of a Variable Power
If:
$$y=u(x)^{v(x)}$$
then:
$$\ln y=v(x)\ln u(x)$$
Hence:
$$y=e^{v(x)\ln u(x)}$$
Usage
- General method for differentiating or evaluating variable-base, variable-exponent expressions.
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