I've hit abit of a roadblock. I was wondering, how would I solve this (using the differntiation rules, not by first principles.) I can't see how to approach this. Could someone show working (such as expanding / factorising) in order to be able to use those rules to solve:
Differentiate with respect to x:
So, take a look at .
It should be clear that this is equivalant to
And that this is equivalent to .
Now, since is common to both terms, I can factor it out giving me
Can you see how this applies to your problem? Do you remember this from algebra. It is calle the Distributive Law. It's a biggie. And you're gonna need it.
Note that there are a whole bunch of ways to differentiate something:
The Quotient Rule is one way we coulda went:
But why go through all that trouble if we coulda simplified the expression first, and the used the power rule, which is so much easier.