Differential Calculus Exam Questions with Latest Update

Differential Calculus Exam Questions
with Latest Update
Average Rate of Change - ANSWER-Slope of two points

Instantaneous Rate of Change - ANSWER-Derivative

Derivative is - ANSWER-the slope of the tangent line at one point

Mean Value Theorem - ANSWER-If a function is both continuous and differentiable on
an interval, then there exists some 'c' in that interval at which the average rate of
change equals the instantaneous rate of change

Normal line - ANSWER-Perpendicular to a tangent line

Definition of Derivative - ANSWER-The limit as h approaches 0 of [f(x+h) - f(x)]/h

A function is not differentiable at - ANSWER-A corner, cusp, vertical tangent, or
discontinuity (point, jump, or infinite discontinuity)

Product rule - ANSWER-"First times the derivative of the second plus second times the
derivative of the first"

Quotient rule - ANSWER-"Bottom times the derivative of the top minus top times the
derivative of the bottom, all over the bottom squared"

Chain rule - ANSWER-"Outside-Inside" Rule

d/dx sin(x) - ANSWER-cos(x)

d/dx cos(x) - ANSWER--sin(x)

d/dx tan(x) - ANSWER-sec²(x)

d/dx sec(x) - ANSWER-sec(x)tan(x)

d/dx csc(x) - ANSWER--csc(x)cot(x)

d/dx cot(x) - ANSWER--csc²(x)

d/dx arctan(x) - ANSWER-1 / (1+x²)

d/dx ln(x) - ANSWER-1 / x