Can i get help to solve for the derivative of f(x)= x^4 +1

- Johan14th

Can i get help to solve for the derivative of f(x)= x^4 +1

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- schrodinger

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- Vocaloid

derivative rule for exponents:
the derivative of x^n is n*x^(n-1)

- Vocaloid

also, the derivative of 1 is 0 since 1 is a constant

- Vocaloid

unless you want to find the derivative using the (x+h) method?

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- Johan14th

just an extra question but would the derivative of theta equal 1|dw:1443659495630:dw|

- Vocaloid

yes

- Vocaloid

(theta can be used like a variable, just like x)

- Johan14th

i tried the x+h method and received a wrong answer so i will try the first way you talked about

- Vocaloid

x + h method will always give the right answer

- Johan14th

i just have problems keeping my division right with powers

- Vocaloid

let's try the x + h method first, then I'll show you the "shortcut method" afterwords

- Johan14th

alright

- Vocaloid

|dw:1443659654089:dw|

- Vocaloid

|dw:1443659860105:dw|

- 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

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

anyhoo, we cancel out the x^4 and the -x^4 next|dw:1443660131464:dw|

- Vocaloid

then we factor out h from the numerator

- Vocaloid

|dw:1443660161997:dw|

- Vocaloid

then we cancel out h to get|dw:1443660211856:dw|

- Vocaloid

then we set h = 0 to get|dw:1443660231771:dw|

- 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

no problem! Later on in class, you'll learn tricks and rules that will make this much easier

- Vocaloid

so, like I promised, I can show you a faster method to get the same answer

- Vocaloid

|dw:1443660442174:dw|

- Vocaloid

the derivative of 1 is 0, since 1 is a constant (no variable attached to it)

- Vocaloid

and, like I said before, the derivative of x^n is n*x^(n-1)

- Vocaloid

|dw:1443660601884:dw|

- Vocaloid

none of that icky x + h stuff, haha :P

- 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

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

yes unfortunately for me this also involves a dozen of cheesy math songs that get stuck in your head all day.

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