Answer:
f'(x) = 3(x−1)²
Step-by-step explanation:
Definition of derivative is:
f'(x) = lim(h→0) [f(x + h) − f(x)] / h
f(x) = (x−1)³, so the derivative is:
f'(x) = lim(h→0) [(x−1+h)³ − (x−1)³] / h
f'(x) = lim(h→0) [(x−1)³ + 3(x−1)²h + 3(x−1)h² + h³ − (x−1)³] / h
f'(x) = lim(h→0) [3(x−1)²h + 3(x−1)h² + h³] / h
f'(x) = lim(h→0) [3(x−1)² + 3(x−1)h + h²]
f'(x) = 3(x−1)²
