Find the derivative using first principles

y=3sqrtx

Can someone help me solve this tks

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- Jun 22nd 2007, 11:22 AMjohntuanIntro Calc
Find the derivative using first principles

y=__3__sqrtx

Can someone help me solve this tks - Jun 22nd 2007, 11:28 AMJhevon
Differentiating using first principles means they want you to use the limit definition of a derivative. There are two equivalent definitions that are used, which one did you learn?

**Definition 1:**

For a function , it's derivative, , at an arbitrary point is given by:

**Defintion 2:**

For a function , it's derivative, , at an arbitrary point is given by:

I think the first definition is what you want, so just plug the pieces into the formula and find the limit. (Do you need help with that?) - Jun 22nd 2007, 11:43 AMjohntuan
i learnt both ways but can you solve it using definition 1 please. And yes i need help, when i plug it in I keep getting stuck.

- Jun 22nd 2007, 11:58 AMJhevon

...........................................Combine the fractions in the numerator

..............................................Now combined the fractions once again

.....................................Now multiply by the conjugate of the numerator over itself (This is a standard approach).

...........Now simplify this

...........Simplify more

............Now we see that the 's cancel

...............Now there's no problem when we take the limit

- Jun 22nd 2007, 12:02 PMjohntuan
ok thanks i see where i messed up