Monkey Rule Practice
Let's try calculating the derivative of our model of the length of the day on the Northern Vermont University -- Johnson campus from earlier in the book.
Recall from earlier activities that the model we came up with is
Let's calculate the derivative using Monkey Rules 0 through 8.
First, let's recognize that g is the sum of two functions
c(x)=726.16546 and s(x)=200.61101*sin(0.01682x-1.32145). Monkey Rule 3/Addition Rule says we can calculate the derivative of g by simply adding the derivatives of c and s. Since c is a constant function c'(x)=0.
Now let's take a look at s(x)=200.61101*sin(0.01682x-1.32145). First of all, since s is the product of a constant function with a sine function, Monkey Rule 6b says we only need to focus on the sine part.
Now, the sine part looks a lot like noah from the previous activity! Indeed, s(x) is the composite function f(g(x)) where f(x)=sin(x) and g(x)=0.01682x-1.32145 each of which are tackled directly by way of Monkey Rules 0 and 5: f'(x)=cos(x) and g'(x)=0.01682.
Using Monkey Rule 8/Chain Rule to put it all together, we get:
Note: I rounded to 5 decimal places there at the end when I multiplied 200.61101 and 0.01682 to obtain 3.37428.
Move on to the next activity to put this to some actual use!