Blog #2 - Mary Graci

This is the second blog of Calculus! Anyway, at the beginning of the week, we reviewed for the Chapter 1 test we had Wednesday. Thursday, we started on derivatives. For derivatives, you use the slope of a tangent line formula. This formula is: lim as x approaches 0 f(x+delta x) - f(x) / delta x

When you are asked to find the derivative, it can be asked in a variety of ways: f'(x), dx/dy, etc.

Ex. 3x
First, plug it into the formula. 3(x+delta x) - 3x / delta x
Then, distribute and simplify. 3x + 3delta x - 3x / delta x
Cancel out whatever you can. 3delta x / delta x
Cancel again to get the delta x out of the denominator, and solve. = 3

Ex. x^2
Again, plug into the formula. (x+delta x)^2 - x^2 / delta x
Distribute and simplify. (x^2 + 2x delta x + delta x^2) - x^2 / delta x
Cancel. 2x delta x + delta x^2 / delta x
Factor out a delta x, then cancel again. delta x(2x + delta x) / delta x = 2x + delta x
Plug in 0 for delta x. 2x + (0) = 2x

Next week, we'll learn a shortcut of how to find a derivative. As for this week, I understood just about everything and I even did really good on my first Calculus test! Anyway, I don't have any questions for this week. Good luck on the upcoming weeks in Calc, everyone!