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math: logarithmic differentiation

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eggy 2021-01-11 21:11:48 -05:00
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@ -605,6 +605,8 @@ $$
\frac{d}{dx}\ln(g(x))=\frac{g´(x)}{g(x)} \frac{d}{dx}\ln(g(x))=\frac{g´(x)}{g(x)}
$$ $$
This opens up the possibility of **logarithmic differentiation**, which is required for exponential or logarithmic functions with a variable base. The **natural logarithm** of both sides should be taken prior to differentiation and logarithmic rules applied to simplify the equation.
### Higher order derivatives ### Higher order derivatives
The **second derivative** of $f(x)$ is the derivative of the first derivative of $f(x)$, that is, $f´´(x)$. The **second derivative** of $f(x)$ is the derivative of the first derivative of $f(x)$, that is, $f´´(x)$.