Common Core · AP Calculus AB
FUN-3.A
AP Calculus AB, Unit 2 — Calculate derivatives of familiar functions (the power rule, sums, polynomials).
A note on this mapping: The Common Core has no calculus standards; this is the AP Calculus AB learning objective.
AP Calculus AB, Unit 2 — Calculate derivatives of familiar functions: e^x, ln x, sin x and cos x.
A note on this mapping: The Common Core has no calculus standards; this is the AP Calculus AB learning objective.
The 2 skills that cover it
- Derivatives & the Power RuleDefine the derivative as an instantaneous rate of change and compute it for polynomials with the power rule.Read the lesson →
- Transcendental DerivativesDifferentiate the functions that are not powers of x: exponentials of any base, logarithms, tangent and secant, their compositions and products, and the inverse of a function at a point.Read the lesson →
What a student should be able to do
- Interpret the derivative as a slope of a tangent line.
- Differentiate a power of x with the power rule.
- Differentiate a polynomial term by term.
- Evaluate a derivative at a point to get a slope.
- Differentiate ekx, bx, ln x and log_b x.
- Derive the derivatives of tan, sec, cot and csc from the quotient rule.
- Apply the chain rule through exponential, logarithmic and trigonometric functions, and use logarithmic differentiation.
- Find the derivative of an inverse function at a point.