Answer the following with reference to the derivative of a function.
MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Answer the following with reference to the derivative of a function.
(i) State what the symbols f′(x) and dxdy represent when y=f(x). Clearly mention the independent and dependent variables involved.
(ii) For y=f(x)=x3, write the derivative at x=2 in both Lagrange and Leibniz notations.
(iii) Express, in words, the meaning of the value obtained in part (ii).