Theory question 103
DifferentiationDifferentiate, with respect to x, x3 − 2x from the first principle
Show the model answer
Model answer
y = x3 − 2x; y + δy = (x + δx)3 − 2(x + δx)
δy = 3x2δx + 3x(δx)2 + (δx)3 − 2δx
δy/δx = 3x2 + 3xδx + (δx)2 − 2
As δx → 0: dy/dx = 3x2 − 2
Explanation
Give x a small increase δx, find δy, divide by δx and let δx tend to 0.