While deriving for a positive integer using the expression

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

Problem

While deriving

\dfrac{d}{dx}(x^{n})

for a positive integer

n

using the expression

\dfrac{(x+h)^{n}-x^{n}}{h}

, the term that remains after cancellation of

x^{n}

and division by

h

is ______. Which option correctly identifies the coefficient of

x^{n-1}

in that term? (a)

n-1

(b)

\dfrac{n(n-1)}{2}

(c)

n

(d)

n^{2}

Related theory

Algebraic Expansion
Differentiation Rules
Differentiation from first principles
Derivatives
Limits and Derivatives

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