2.2 basic differ rules and rates of change

Question 1

What do the sum and difference rules mean?

Answer 1

The derivative can be taken term by term

Question 2

What is the derivative of e^x and why?

Answer 2

Because e is already a rate of change

Question 3

What is the power rule and how is it derived?

Answer 3

If f(x)=x^n, then f’(x)=n•x^(n–1)
Derived from derivative definition, then pascals triangle (n choose 0)x^n+(n choose 1)x^(n-1)[change in x]+•••
Then, divide out change in x and set change in x to 0