How do you differentiate #f(x)=e^(x^2-3x^2-4) # using the chain rule?
The chain rule states that when differentiating a function that contains another function inside of it, the following happens: (1) differentiate the outside function and leave the inside function intact. (2) Multiply this by the derivative of the outside function.
The chain rule can be written as
Here, we have
Since the derivative of the outside function
Which is (the simplified version of) what we began with. Now, we just need to multiply this by the derivative of the inside function,