3.5 Derivatives of Periodic Functions, 9.3 Partial Derivatives & 9.4 Computing Partial Derivatives Algebraically

Main Points:
The derivative of the sin function is the cos function. This is true because the slopes of these functions are periodic. The partial derivative is the slope of a function dependent on one variable (x or y). The partial derivative can be written as (f (a+h, b) - f (a, b))/h this can be used to find the partial derivative from a data table. This method can also be used on a contour diagram. All one must do is find the interval between contours and the difference between them in the x or y direction. To find the partial derivative of a function algebraically, one must plug in the value for x or y that is static, and then find the derivative of the function after that value has been substituted in. Since the result of a partial derivative is a function itself, you can find the 2nd order partial derivative of that function too. Also, f ' (x,y) (a,b) = f ' (y,x) (a,b).

Challenges:
The second order partial derivative is a little bit confusing. I understand the concept of a derivative of a derivative or how fast the slope is increasing. It's kind of like an acceleration. The part that I was having slight troubles with was just how that concept applies to a second derivative. I just don't understand if this is saying how fast the x increases in terms of y or what. I just need some clarifying on what it basically means.

Reflections:
When thinking about 2nd derivatives while I was writing the Challenges section, I thought that a really good way to think of a 2nd derivative is that it's like an acceleration (yes I'm taking physics). Acceleration is exactly what a 2nd derivative is because it's how fast your position changing is changing.