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Question
Hey i was wonder how you find the derivative of square root x+1 by using the f(x+h)-f(x)/h
If would be found by actually carrying out the function.
That is, [√(x+h+1) - √(x+h)]/h.
To determine what this is, multiply the top and bottom by the conjugate of the top.
That is, multiply the top and bottom by [√(x+h+1) + √(x+h)].
Note that multiplying by the conjugate would give x+h+1 - x-1 = h on top.
This cancels with the h on the bottomm, and the other h's can be let go to 0.
This would give 1/[2√(x+1)] as the answer.
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