Is the equation we will use to demonstrate correct use of the chain rule.
The equation at the core of the chain rule is:
Seeing that dt as a numerator and dt as a denominator are both present in the equation allows us to cancel dt from the equation.
When using the chain rule, firstly, we must express f(x) using a simpler power of e, to do this we set t equal to x2+2, giving us the following equalities.
From our differentiation rules we know that:
Finally, we substitute into dy/dx=dt/dx*dy/dt