Blog #7

Ok this week was pretty much a review of derivatives, but we also learned how to solve related rate problems. Well, truthfully, I didn't learn how to do the related rate stuff, I just kinda went with the flow of class, I don't think anybody really understood how to do those problems this week, and we have an exam tomorrow. Ooh this is gonna be fun :/ Anyway, I'll review some "simple" derivative work.

Find the derivative of sin y. Find the largest interval about the origin for which y is a differentiable function of x.

sin y = x

cos y (dy/dx) = 1

dy/dx = (1)/(cos y)

pi/2 is less than y is less than 3 pi/2

Determine the slope of the tangent line to the graph of x^2 + 4y^2 = 4 at (sqrt(2), -1/sqrt(2))

2x + 8y(dy/dx) = 0

8y(dy/dx) = -2x

dy/dx = -2x/8y

dy/dx = -2(sqrt(2)/8((-1)/(sqrt(2))) = 2(2)/8 = 4/8 = 1/2

slope = 1/2

Like I said on the top of the blog, I don't understand the rate of change problems. And with this exam coming up TOMORROW, i don't know what's gonna happen, but oh well.