Question

(x-1)³ find derivative using definition​

Answer 1

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

Answer 2

Step-by-step explanation:

definition of the derivative to differentiate functions. This tutorial is well understood if used with the difference quotient .

The derivative f ' of function f is defined ascthe above pic.

when this limit exists. Hence, to find the derivative from its definition, we need to find the limit of the difference quotient.