Find the derivative using first principles
y= 3
sqrtx
Can someone help me solve this tks
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?)
...........................................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