For the function

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

For the function

f(x)=x^{4}

, respond to the questions below. (i) Write the difference quotient that gives the derivative

f'(x)

. (ii) Use your expression in part (i) to find the exact value of

f'(2)

. Show all necessary algebraic steps before taking the limit.

Related theory

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

Browse the problem library