SOLUTION: find the derivative of (x-2)^2/x using the limit definition? I used the derivative rules and got 2(x-1)/x but when I do it with the definition I get 2x-2/x so I am wondering where

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: find the derivative of (x-2)^2/x using the limit definition? I used the derivative rules and got 2(x-1)/x but when I do it with the definition I get 2x-2/x so I am wondering where      Log On


   

Question 945530: find the derivative of (x-2)^2/x using the limit definition?
I used the derivative rules and got 2(x-1)/x but when I do it with the definition I get 2x-2/x so I am wondering where I went wrong.Here's what i have so far
limt f(x+h)-f(x)/h
(x+h-1)^2/(x+h)-(x-1)^2/x/h
= x(x+h-1)-(x-1)^2(x+h)/(x+h)(x)
I tried cross multiplying them and then foil the values in the brackets that are to the power of two but I seem to be doing something wrong. Could someone show how to do this step-by-step and explain it. that would be great
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
Your work shows misidentifying placement of parentheses, and this as well as other symbolism & viewing difficulties are reasons why we use the Derivative or Differentiation Rules instead of always taking the lowest level using the Difference Quotient. You just NEED to watch all your steps VERY VERY carefully if using the Difference Quotient (as well as if using the Differentiation Rules).

Rechecking your given expression, not precise which it really is.
Either you mean 2x-2%2Fx OR %282x-2%29%2Fx OR 2%28x-2%29%2Fx.
Students often mishandle this, so asking now.
If I knew which you meant, I might try this on paper as a way to start help.