Stephen's Blog #3

Okay, so I loved this week because we only had 4 days! Yay. I would like to say that I actually like working with derivatives. They are pretty easy to me, as far as we got on them so far at least haha. Anyway, we went further into derivatives this week and we learned some rules.

The Constant Rule

When you are trying to find a derivative and there is a constant, the derivative of a constant is 0.

The Power Rule

Every time you take a derivative, you lose a power.

So, if you have an exponent, you multiply it by the coefficient and then subtract 1 from the original exponent. Ex. (x^3 would become 3x^2)

Also, we learned how to take derivatives of sine and cosine.

For sin x, the derivative is cos x. For cos x, the derivative is -sin x.

Example:

Find the derivative of (5)/(2x^2).

You would rewrite it as 5/2 x^-2.

Now multiply -2 by 5/2 and you get -5 and raise x^-3 because you subtracted 1. (-5x^-3)

Now just simplify it by writing it as (-5)/(x^3)

The only thing I don't really understand is differentiability. Like where is it differentiable, where is it not.