How to know when to use what rule in Differentiation?

shizz

I'm not a beginner at Differentiation and I can usually spot when to use what rule for different equations but sometimes I just get confused and use the wrong one. I was just wondering if anyone can point me towards a useful guide on how to know when to use which rule?

Thanks

sponsoredwalk

Could you post a few examples of questions you're confused about along
with your thoughts on each equation & what you see as the possibilities?
If you do that we could tell you why possibility A, B, C & D are wrong while
possibility E is the way to go :cool:

TheBody

I'm guessing you are asking when to use the product, quotient and chain rule?

For the product rule, you use it when you have two things being multiplied together...i.e a product!!

For the quotient rule, you use it when you are dealing with a fraction type problem. (Quotient is just a fancy word for a fraction)

For the chain rule, you use this when you have a composition of functions. What I usually say, is to use this rule when you are sure it's not a product or quotient rule problem. So, use a process of elimination.

shizz

Sorry guys I don't really have any problems that I am stuck on I was just hoping someone might know of a place where there was a sort of guide on how to spot it. It's more so with larger equations. I think I'm getting the hag of it now though and not making the mistakes I used to.

sponsoredwalk

It's highly likely that you're getting confused with larger equations
because you don't know how to break it up & don't know how what
rule can be used in what situation or why.

Here is a list of the possibilities:

01: Derivative of a Constant
02: Derivative of a Constant Times a Function
03: Derivative of a Sum
04: Derivative of a Product
05: Derivative of a Quotient
06: Power Rule for Natural Powers
07: Power Rule for Integer Powers
08: Power Rule for Rational Powers
09: Power Rule for Real Powers
10: The Chain Rule
11: Derivative of an Inverse Functions
12: Implicit Differentiation
13: Parametric Differentiation

What you should notice about the list I gave is that rules 6-9 are basically
the same rule. Here is a list of some of the special functions that come up
along with their derivatives.

My advice is to watch the videos on this & this website that correspond to
the list I gave you so that you can hear someone explain what's going on
in each situation & give you the intuition. Once you've done this you'll
never look at "larger equations" as something scary because you will
know how to break it all up into small chunks, each small chunk being
solvable by one of the methods in this list.

Once you've done this, if you want to test yourself, I personally find that
taking the second derivative of some big implicit differentiation problem
is the biggest thing you'll run into, try some of those problems along with
general differentiation problems.

I'll just point out that all you really need to worry about is the quotient
rule & the chain rule really, everything else should be totally obvious if
you're able to recognize what you need to do when you see an equation.