#Ap calculus chain rule quiz how to
#Ap calculus chain rule quiz full

Integration and Accumulation of Change-Finding accumulations of change, Reimann sums, and definite integrals, understanding the Fundamental Theorem of Calculus, interpreting accumulation functions, finding anti-derivatives and indefinite integrals, and integrating using substitutions, long division, and completing the square.

Analytical Applications of Differentiation-Understanding the Mean Value Theorem, using the Extreme Value Theorem, finding global and local extrema, applying the First Derivative Test and Second Derivative Test, finding intervals of increase and decrease, understanding concavity, sketching graphs, solving optimization problems, and using implicit relations.

Contextual Applications of Differentiation-Interpreting derivatives in context, using rates of change in motion and other context, applying related rates, approximating using linearization, and applying L’Hospital’s Rule.

Differentiation: Composite, Implicit, and Inverse Functions-Applying the Chain Rule, using implicit differentiation, differentiating inverse functions, and calculating higher order derivatives.

Differentiation: Definition and Basic Rules-Defining average and instantaneous rates of change, defining the derivative of a function, estimating derivatives at a point, connecting differentiability and continuity, applying the Power Rule, the Product Rule, and the Quotient Rule, and determining derivatives of constants, sums, differences, and constant multiples, trigonometric functions, e x, and ln x.

Limits and Continuity-Defining limits, estimating limits from graphs and tables, determining limits using algebraic properties and manipulation, applying the Squeeze Theorem, Determining types of discontinuities, understanding asympototes, and the applying Intermediate Value Theorem.

You should be familiar with the following topics:

The College Board is very detailed in what they require your AP teacher to cover in his or her AP Calculus AB course. If you score high enough on the exam, your AP Calculus score could earn you college credit!Ĭheck out our AP Calculus AB Guide for the essential information you need for the exam:

#Ap calculus chain rule quiz full

For full details, please click here.Īre you familiar with the Mean Value Theorem? Can you calculate derivatives? The AP ® Calculus AB exam tests topics and skills discussed in your AP Calculus AB course. Always keep in mind the 3-step process:COVID-19 Update: To help students through this crisis, The Princeton Review will continue our 'Enroll with Confidence' refund policies.

Use the Chain Rule to find the derivative of a composition. Now that we have found the derivative correctly, let’s simplify the final answer using algebra.

Finally, multiply by the derivative of the inside:.

First find the derivative of the outside:.

Just don’t forget that step of plugging back in u = g( x). Here, the rule has been written in Leibniz notation, and clearly expresses the fact that the derivative of a composition is really just the product of the derivatives of the individual functions.

Multiply by the derivative of the inside.Įquivalently, if y = f( u), and u = g( x), then.

Then the composite function, f( g( x)) is also differentiable, and Suppose f and g are differentiable functions. (Inside function, or g( x)): u = 4 x – 2. (Outside function, or f( u)): y = u 3, and To make it clearer, we often use a different variable name, such as u, for the input variable of the outside function.įor example, if y = (4 x – 2) 3, then the most natural decomposition would be:

#Ap calculus chain rule quiz how to

In other words, you have to learn how to decompose a composite function into a pair of functions - the outside and inside functions. To use the Chain Rule properly, you need to know how to go the other direction. We might call f the “outside” function, and g the “inside” function.įor example, if f( x) = sin( x), and g( x) = x 2 + 1, then their composition is: If f( x) and g( x) are two functions, then we call f( g( x)) the composition of f and g. We use the Chain Rule to find the derivative of a composition of functions, that is a function of the form f( g( x)). If so then I hope that by the end of this short article, you’ll gain a better appreciation for the Chain Rule and how it is used in derivative problems. Many students dread the rule, think that it’s too difficult, don’t fully understand where to apply it, and generally wish that it would go away. Of all the derivative rules it seems that the Chain Rule gets the worst press.