derivatives chain rule Calculus I Ms. Plata

Chain Rule: Suppose you are asked to differentiate the function The differentiation formulas that you leaned in the previous sections do not enable you to calculate f’(x)…

Then… If f and g are both differentiable and F=fog is the composite function defined by F(x)=f(g(x)), then F is differentiable and F’ is given by the product In Leibniz notation, if y=f(u) and u=g(x) are both differentiable functions, then

In using the Chain Rule we work from the outside to the inside. We differentiate the outer function f and then we multiply by the derivative of the inner function.

Example: function function function Outer Evaluated at Derivative Evaluated Derivative function inner function of outer at inner of inner function function function

Example: Differentiate: This would be really difficult without the Chain Rule Taking and n= 100, we have:

Now, let’s do some exercises where we are going to apply everything we have learned this week! Remember: Do as many exercises as you can…repetition is very important!!!