Normally when we differentiate equations like this to get :
..we expand the bracket, and then differentiate.
Chain rule is a shortcut way of differentiating sh*t equations like this to get :
We do NOT want to do this:
..because that will take like 3 hours expanding and simplifying.
In chain rule, we change whatever’s inside the bracket to another variable (that isn’t or ), like this:
For this equation :
..we have 2 equations now, and we can differentiate the second equation ():
(simple differentiation)
And we can also differentiate the first equation ().
(also simple differentiation)
We are left with , and in the end.
What we are trying to get is .
To do this, we can write it like this:
Since is the same on both sides, we can cancel it out (Note: it isn’t exactly the process of cancelling.).
Now, we remove the :
Through this, we have differentiated this sh*t equation of into , using chain rule, instead of having to do this:
Normally the L3 Differentiation exam don’t require students to simplify the equation (because that will take more than 3 years), so leaving the answer as should be fine (unless told to otherwise).