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Derivative Criterion for Constant Ratio
For non-zero differentiable functions:
$$\frac{f'(x)}{f(x)}-\frac{g'(x)}{g(x)}=0$$
implies:
$$\frac{f(x)}{g(x)}=C$$
Usage
- Used to recognize when the ratio of two functions remains constant.
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Derivative Criterion for Constant Ratio
For non-zero differentiable functions:
$$\frac{f'(x)}{f(x)}-\frac{g'(x)}{g(x)}=0$$
implies:
$$\frac{f(x)}{g(x)}=C$$
Usage
- Used to recognize when the ratio of two functions remains constant.
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