Let , being a non-negative integer. The value of for which the equality is valid for…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let

f(x) = x^n

n

being a non-negative integer. The value of

n

for which the equality

f'(x+y) = f'(x) + f'(y)

is valid for all

x, y > 0

, is (1) 0, 1 (2) 1, 2 (3) 2, 4 (4) None of these

Related theory

Functions
Differentiation Rules
Rules of differentiation
Intuitive idea of derivatives
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