Chain Rule

Our detested rule, working hard every day to make every problem just that tiniest bit harder (or, who am I kidding, way harder) in it’s confounding nested ways, lets discuss this bringer of pain.

What is chain rule?

When you’ve got a function inside a function (f(g(x))), and you decide that you must take the derivative of it, chain rule is forced upon your soul, as it is the method used in these situations

The Method

The derivative of f(g(x)) is (f prime (g(x)) * g prime (x)), illustrated below,

But did you think it ended there? No no, that’s chain rule for those not tortured in life, what we will see is nested chain rule, which is just following the same process but ends up getting pretty confusing, make sure you know exactly how it works before it ends up on your tests in it’s great fashion

Conclusion

Yup, that was shackle rule, our one true friend, hope this got you back on track!