Section 3.1

Let’s review the chain rule.

In other words, the derivative of something squared equals two times the something, times the derivative of the something. Therefore, if we call the inside function y, we can write

Here is the derivative of the inside function y.

Similarly,

Whenever the variable in your function is different from the variable you are differentiating with respect to, you must remember to multiply by the derivative of the inside function. Another example:

, but

For problems like 3-18, the author tells you to use implicit differentiation. I won’t tell you that on a test. The reason you know to use implicit differentiation is because the equation is not solved for y.

You are responsible for reproducing the proof of the power rule for rational exponents (also called "the new, improved power rule with flouride") on a test.