#Derivative of log how to
We can define a compound logarithm rule that tells us how to approach situations like this, with multiple factors being multiplied and divided: How do these help? Well notice that our problem consists of a logarithm of the product of factors in the numerator, divided by the product of some other factors in the denominator. The first rule tells us how to expand the log of a product, the second the log of a quotient, and the third the log of a power. Just to briefly review the rules of logarithms (and \(ln\), which is a specific type of logarithm), the important ones are: Basically, if you see a problem like this and don't know the trick, you're better off skipping it entirely.īut let's not do that! The trick is to use the rules of logarithms to expand, or rewrite the function before we even mention the word "derivative." There, I said it.
The hint provides a glimpse of comfort, if only we can figure out the "easy way." If not, we'll be doing chain rules inside product rules inside quotient rules inside chain rules all night, run out of time, and probably fail the exam.
#Derivative of log full
Its full of exponents and natural logs and square roots, all jammed up against one another in some night-before-the-test anxiety dream. This function, frankly, looks terrifying. Hint: There is an easy way, and a hard way to approach this problem. Case in point, our calculus problem this evening:
This visual intimidation factor is something that breeds anxiety, induces brain farts on tests, and ultimately turns a lot of people off to math. Sometimes, it just looks overwhelming, even when you actually know how to do it.