Mai Someya- Blog Post 4

Hi class,
I'm here to teach a something fun that can help remember everyones least favorite derivate rule.. THE CHAIN RULE. We are going to think of the chain rule like a sandwich because everyone loves sandwiches right???
Recall: the chain rule is used when finding the derivate of a function within a function and by definition the chain rule is: h(x)=f(g(x)), h'(x)=f'(g(x))(g'(x))
Example: Find the derivate of the equation h(x)= 3(x^4+1)^3
So what do all sandwiches need? THE BREAD! And we all know that there are two slices of bread to each sandwich that hold the inside together. So lets find the bread of this derivative!

Top bread a.k.a the DERIVATIVE of the outside function
Bottom bread a.k.a the DERIVATIVE of the inside function

Ya see where I'm going with this? if not just keep following along..

The filling will be the given function of the inside function
Starting to see the sandwich?

So.. DERIVATIVE       BREAD
        normal f(x)              filling
       DERIVATIVE       BREAD

We can apply to our original problem.
derivative of the outside= f(x)=3x^3    f'(x)=9x2
derivative of the inside= g(x)=x^4+1      g'(x)=4
inside function= g(x)=x^4+1
Now make a derivative sandwich!!!
DERIVATIVE        f'(x)=9x2
   normal f(x)            g(x)=x^4+1
 DERIVATIVE        g'(x)=4

Combine all the ingredients together and you get…
9(x^4+1)(4)

Tadaaa! you have you're very own chain rule sandwich. Enjoy!