3.1 Derivative Formulas for Powers and Polynomials & 3.2 Exponential and Logarithmic Functions

Main Points
The derivative of a constant function is always the same. The same is true of a Linear Function. If a function is multiplied by a constant, so is the derivative. The derivative of two functions added together is equal to the derivative of each separate function added together. The power rule states that d/dx (x^n) = nx^n-1. Differentiation is used to find the equation of a line tangent to a slope. If you graph the derivatives of 2^x or 3^x etc. you will see that the derivative graph looks like the original function, but stretched upward. This means that the derivative must be simply the function multiplied by a number. e^x = e^x. e approximately equals 2.718. The exponential rule states that d/dx (a^x) = (ln a)a^x. The derivative of ln(x) = 1/x.

Challenges
The exponential rule is a little mysterious, the solution is more complex than what the book gave, but maybe that's because they don't want to confuse us too much. Anyway, e and natural log just overall I don't know much about, so it's a little confusing. My problem is just not knowing enough about log and e and how they originated.

Reflections
Well now we can solve those pesky derivative problems quicker. I'm understanding everything. I've seen all of this material before, so it's not a problem. I really enjoyed going over the manual ways of finding derivatives and other things, because it makes it relavant, but now we forge on to the land of straight up math, but I think we'll still be able to apply it to the real world easily. I just liked to see how the math methods were made in the first place.