Probably the most interesting part of this section is the way the power rule works to find the derivative. I feel like this section is pretty straightforward and really just builds on section 3.1 giving more tools to make solving derivatives even easier.
Problem:
1. Find the derivative of (7x^9 + square root x + 3x^(5/8)).
I used a combination of the power rule and sum rule to solve this derivative. The sum rule says that you can take the derivative of each piece of the function individually. Starting with 7x^9, I used the power rule to move the 9 down in front of the x, then I subtracted 1 from the exponent 9. This gave me 7*9x^8. The square root of x is equal to x^(1/2) so I used that instead, and applied the power rule. This gave me 1/2x^(-1/2). For 3x^(5/8) I used the power rule again, moving 5/8 down in front of x and subtracting 1 from 5/8. This gave me 3*(5/8)x^(-3/8). Put together, the derivative of this function is 63x^8 + (1/2)x^(-1/2) + (15/8)x^(-3/8)
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