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derivative rule for exponents: the derivative of x^n is n*x^(n-1)
also, the derivative of 1 is 0 since 1 is a constant
unless you want to find the derivative using the (x+h) method?
just an extra question but would the derivative of theta equal 1|dw:1443659495630:dw|
(theta can be used like a variable, just like x)
i tried the x+h method and received a wrong answer so i will try the first way you talked about
x + h method will always give the right answer
i just have problems keeping my division right with powers
let's try the x + h method first, then I'll show you the "shortcut method" afterwords
now, if you're wondering how I got from (x+h)^4 to that huge expression, I used Pascal's triangle (if you don't know it already, I highly suggest learning about it! it saves tons of time)
we've barely seen it in class, weird enough it was for engineering and not calculus, but now i will try to learn it ahead of time. thank you
anyhoo, we cancel out the x^4 and the -x^4 next|dw:1443660131464:dw|
then we factor out h from the numerator
then we cancel out h to get|dw:1443660211856:dw|
then we set h = 0 to get|dw:1443660231771:dw|
alright i think i finally got a hand of this. i was just really confused in class but this explains everything nice and easy thanks again.
no problem! Later on in class, you'll learn tricks and rules that will make this much easier
so, like I promised, I can show you a faster method to get the same answer
the derivative of 1 is 0, since 1 is a constant (no variable attached to it)
and, like I said before, the derivative of x^n is n*x^(n-1)
none of that icky x + h stuff, haha :P
Haha well this just made my hour of calculus struggle and the 10 trees i had to sacrifice for the paper really lame ...
I had to do that, too, lol. I think most calc teachers start off with the x + h method just to emphasize the idea of what a derivative really is (the rate of change over a small interval h)
yes unfortunately for me this also involves a dozen of cheesy math songs that get stuck in your head all day.