Alaina's blog, 5 Sept. 2010

This week, well starting Wednesday, we learned derivatives. They are used to find the slope of a graph or just to find the derivative and are pretty simple.

Notation for Derivative:

-Slope of a tangent line equals a derivative

1. ^dy/_dx
2. y¹
3. f¹(x)
4. ^d/_dx[f(x)]
5. Dx[y]

Basic Formulas:

Slope of a secant line: ^{f(x+Δx)-f(x)}/_Δx

Slope of a tangent line: _lim^{f(x+Δx)-f(x)/_Δx}

^2->0

Ex 1: find the slope of th egraph of f(x)=2x-1 at (2,1)

_{lim =}^{2(x+Δx)-1(2x-1)}/_Δx

^x->0

=^{2x+2Δx-1-2x-1}/_Δx

=^2Δx/_Δx

=Δx

Ex 2: Find the derivative of f(x)=x²+4x

_{lim =} (x+Δx>²+4(x+Δx)-(x²+4x)/_Δx

^x->0

=x²+2Δxx+Δx²+4x+4Δx-x²-4x/_Δx

=4Δx

I'm not really sure whether or not I did the last one correctly, but I think that I did. If I did not, feel free to correct my work.