AP Calculus AB, unit: Differentiation: Composite, Implicit, and Inverse Functions. Conceptual understanding and key rules for this unit, explained in plain language alongside the formula. Front: a concept or short problem cue. Back: the explanation, rule, or answer.
38 cards · basic cards · AI-written, checked twice. Edit anything.
- What is the Chain Rule used for?
Show answer
Finding the derivative of a composite function- What is the Chain Rule formula?
Show answer
The derivative of f(g(x)) is f'(g(x)) times g'(x)- What is a composite function?
Show answer
A function formed by applying one function to the result of another- How do you differentiate a function raised to a power, like (g(x))^n?
Show answer
Using the Chain Rule: n times (g(x))^(n-1) times g'(x)- What is implicit differentiation used for?
Show answer
Finding the derivative of y with respect to x when y is not isolated in the equation- What is the key extra step in implicit differentiation involving y?
Show answer
Multiplying by dy/dx whenever differentiating a term containing y- What is an inverse function?
Show answer
A function that reverses the effect of the original function- What is the relationship between the derivatives of inverse functions?
Show answer
The derivative of the inverse at a point is the reciprocal of the original function's derivative at the corresponding point- What is the derivative of arcsin(x)?
Show answer
1 divided by the square root of (1 minus x squared)- What is the derivative of arctan(x)?
Show answer
1 divided by (1 plus x squared)- What is logarithmic differentiation used for?
Show answer
Simplifying the differentiation of products, quotients, or variable exponents by taking a logarithm first- What is the derivative of a^x, where a is a constant?
Show answer
a^x times the natural log of a- Why is implicit differentiation necessary for a circle equation like x squared plus y squared equals r squared?
Show answer
y cannot be easily isolated as a single explicit function of x- What is a higher-order derivative?
Show answer
A derivative of a derivative, such as the second or third derivative of a function- What does the second derivative represent?
Show answer
The rate of change of the first derivative, often related to concavity
FlashKeepers