Let be a positive integer

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let

n

be a positive integer. (a) State the binomial theorem expansion of

(x+h)^{n}

up to and including the term containing

h^{2}

. (b) Hence prove that the derivative of

x^{n}

with respect to

x

n x^{n-1}

. (c) Using the result of part (b), obtain the derivative of

x^{3}

and verify that it equals

3x^{2}

Related theory

Binomial Theorem
Derivative Foundations
Differentiation from first principles
Intuitive idea of derivatives
Limits and Derivatives

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