Johan14th
  • Johan14th
Can i get help to solve for the derivative of f(x)= x^4 +1
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Vocaloid
  • Vocaloid
derivative rule for exponents: the derivative of x^n is n*x^(n-1)
Vocaloid
  • Vocaloid
also, the derivative of 1 is 0 since 1 is a constant
Vocaloid
  • Vocaloid
unless you want to find the derivative using the (x+h) method?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Johan14th
  • Johan14th
just an extra question but would the derivative of theta equal 1|dw:1443659495630:dw|
Vocaloid
  • Vocaloid
yes
Vocaloid
  • Vocaloid
(theta can be used like a variable, just like x)
Johan14th
  • Johan14th
i tried the x+h method and received a wrong answer so i will try the first way you talked about
Vocaloid
  • Vocaloid
x + h method will always give the right answer
Johan14th
  • Johan14th
i just have problems keeping my division right with powers
Vocaloid
  • Vocaloid
let's try the x + h method first, then I'll show you the "shortcut method" afterwords
Johan14th
  • Johan14th
alright
Vocaloid
  • Vocaloid
|dw:1443659654089:dw|
Vocaloid
  • Vocaloid
|dw:1443659860105:dw|
Vocaloid
  • Vocaloid
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)
Johan14th
  • Johan14th
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
Vocaloid
  • Vocaloid
anyhoo, we cancel out the x^4 and the -x^4 next|dw:1443660131464:dw|
Vocaloid
  • Vocaloid
then we factor out h from the numerator
Vocaloid
  • Vocaloid
|dw:1443660161997:dw|
Vocaloid
  • Vocaloid
then we cancel out h to get|dw:1443660211856:dw|
Vocaloid
  • Vocaloid
then we set h = 0 to get|dw:1443660231771:dw|
Johan14th
  • Johan14th
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.
Vocaloid
  • Vocaloid
no problem! Later on in class, you'll learn tricks and rules that will make this much easier
Vocaloid
  • Vocaloid
so, like I promised, I can show you a faster method to get the same answer
Vocaloid
  • Vocaloid
|dw:1443660442174:dw|
Vocaloid
  • Vocaloid
the derivative of 1 is 0, since 1 is a constant (no variable attached to it)
Vocaloid
  • Vocaloid
and, like I said before, the derivative of x^n is n*x^(n-1)
Vocaloid
  • Vocaloid
|dw:1443660601884:dw|
Vocaloid
  • Vocaloid
none of that icky x + h stuff, haha :P
Johan14th
  • Johan14th
Haha well this just made my hour of calculus struggle and the 10 trees i had to sacrifice for the paper really lame ...
Vocaloid
  • Vocaloid
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)
Johan14th
  • Johan14th
yes unfortunately for me this also involves a dozen of cheesy math songs that get stuck in your head all day.

Looking for something else?

Not the answer you are looking for? Search for more explanations.