1. derivatives chain rule
Calculus I Ms. Plata

2. 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)…

3. 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

4. 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.

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

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

7. 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!!!