- #1
s3a
- 818
- 8
Homework Statement
Given f(x) = x^(2/3), find f'(x) using the Δ method.
Homework Equations
f'(x) = (f(x + Δx) – f(x))/(Δx)
The Attempt at a Solution
I understand the entire solution (that is attached along with the problem as a png file), except how to get [(x + Δx)^(4/3) + (x + Δx)^(2/3) x^(2/3) + x^(4/3)]/[(x + Δx)^(4/3) + (x + Δx)^(2/3) x^(2/3) + x^(4/3)] = 1, without looking at the solution.
How would I come up with that on my own? What's “playing tricks with my head” is the fractional exponents. If it were dealing with square roots, for example, I would simply multiply the numerator and denominator by the conjugate of the numerator.
Any input would be GREATLY appreciated!