I'm attempting to find the derivative of the function:
$$f(x) = 4x^2+3x+5$$
Using the alternative formula:
$$\frac{f(z)-f(x)}{z-x}$$
Here are my steps so far:
$$\frac{4z^2+3z+5-(4x^2+3x+5)}{z-x}$$
$$\frac{4(z^2-x^2)+3(z-x)}{z-x}$$
I have no idea where to go from this point. I've tried several different things to come up with the correct answer – which I know is $8x+3$. Can someone please guide me through this problem? I'm completely stuck.
Also, sorry about the formatting. I'm using this editor http://www.codecogs.com/latex/eqneditor.php?lang=en-en
and don't have it completely figured out yet.
Best Answer
Use the difference of two squares:
$$z^2-x^2 = (z-x)(z+x)$$