Using the limit definition, how do you differentiate f(x) = x^(1/2) ?
1 Answer
Dec 28, 2015
The crucial step is
Explanation:
Here is the algebra of the crucial step of "rationalizing" the numerator:
# = ((x+h)-x)//(h((x+h)^(1/2) + x^(1/2)))
= h/(h((x+h)^(1/2) + x^(1/2)))
Using this algebra, we get:
= lim_(hrarr0) 1/((x+h)^(1/2) + x^(1/2))
= 1/(x^(1/2)+x^(1/2)) = 1/(2x^(1/2))