Question

How to do big chain rules?? (when lots of derivatives are given)

a) Apply the Product Rule
b) Apply the Chain Rule
c) Apply the Quotient Rule
d) Apply the Power Rule

Answer 1

To do big chain rules, apply the Chain Rule. Follow the steps: identify the inner and outer function, find their derivatives, and multiply them together.

Step-by-step explanation:

To do big chain rules, you need to apply the Chain Rule. The Chain Rule allows you to differentiate composite functions. Here are the steps:

1. Identify the function inside the function. This is called the inner function, denoted as u.
2. Find the derivative of the inner function with respect to the independent variable (du/dx).
3. Identify the outer function, denoted as g(u).
4. Find the derivative of the outer function with respect to the inner variable (dg/du).
5. Multiply the derivatives obtained in steps 2 and 4 together to find the derivative of the composite function (dy/dx = (dg/du) * (du/dx)).

Remember that you may need to apply other derivative rules, such as the Product Rule or Quotient Rule, within each step if necessary.