CramX
RegisterLog in
Back to AI Flashcard MakerMathematics /AP Calculus AB: 5.3.3 Using the Derivative Rules with Transcendental Functions

AP Calculus AB: 5.3.3 Using the Derivative Rules with Transcendental Functions

Mathematics8 CardsCreated 3 months ago

This flashcard set focuses on applying derivative rules—such as the product, quotient, and chain rules—to transcendental functions like exponential, logarithmic, and trigonometric expressions. It emphasizes how to handle complex combinations of functions, especially when multiple layers of composition require repeated application of the chain rule.

PrintEmbedImportReport

Using the Derivative Rules with Transcendental Functions

  • Some functions are combinations of other functions, such as products or quotients. To differentiate these functions, it may be necessary to use several computational techniques, possibly more than once.

  • Transcendental functions have unusual derivatives.

Tap or swipe ↕ to flip
Swipe ←→Navigate
1/8

Key Terms

Term
Definition

Using the Derivative Rules with Transcendental Functions

  • Some functions are combinations of other functions, such as products or quotients. To differentiate these functions, it may be necessary to...

note

  • A transcendental function is a function that cannot be
    expressed in terms of a variable raised to a power. You can use all of the differ...

Calculate the slope of the line tangent to f (x) = 1 + e^2x at x = 0.

2

Find f′(x) if f(x)=cos(2x^2).

f′(x)=−4xsin(2x^2)

Suppose f(x)=2^(x^2−2x). Find f′(1).

f′(1)=0

Suppose f(x)=log_7x^2.What is the slope of the line tangent to f where x=2?

m=1/ln7

Log in to view all terms

Related Flashcard Decks

Mathematics

Essential SAT Math Formulas

This deck covers key formulas and concepts essential for the SAT Math section, including slope, distance, and vertex forms.

10 cards
View Deck
Mathematics

Algebra 1 Unit 1 Mastery Test

These properties of equality help maintain balance in an equation when performing the same operation on both sides. Inverse operations, like using addition to undo subtraction, are key tools in solving equations.

29 cards
View Deck
Mathematics

ATI TEAS Test Practice Mathematics Part 2

This flashcard set includes a variety of practical math questions covering percentages, conversions, averages, scale drawings, and basic algebra. It’s designed to strengthen problem-solving skills for real-life and standardized test situations.

53 cards
View Deck
Mathematics

ATI TEAS Test Practice Mathematics Part 1

This flashcard set includes a variety of practical math questions covering percentages, conversions, averages, scale drawings, and basic algebra. It’s designed to strengthen problem-solving skills for real-life and standardized test situations.

55 cards
View Deck
Mathematics

Unit 2 Progress Check: MCQ Part A

To determine the point where the tangent line to the graph of the function 𝑓f has a slope of 2 for 𝑥 >0 x>0, we use the fact that the slope of the tangent line at any point is given by the derivative 𝑓′(𝑥)f′(x).

15 cards
View Deck
Mathematics

Customary Liquid Measurement Units

This set of flashcards outlines key relationships between customary units of liquid measurement, including pints, cups, quarts, and gallons. It provides conversion facts to help understand how these units relate to one another in the U.S. measurement system.

3 cards
View Deck

Study Tips

  • Press F to enter focus mode for distraction-free studying
  • Review cards regularly to improve retention
  • Try to recall the answer before flipping the card
  • Share this deck with friends to study together
AP Calculus AB: 5.3.3 Using the Derivative Rules with Transcendental Functions
TermDefinition

Using the Derivative Rules with Transcendental Functions

  • Some functions are combinations of other functions, such as products or quotients. To differentiate these functions, it may be necessary to use several computational techniques, possibly more than once.

  • Transcendental functions have unusual derivatives.

note

  • A transcendental function is a function that cannot be
    expressed in terms of a variable raised to a power. You can use all of the different derivative rules when working with transcendental functions.

  • To find the derivative of a composition of a composite function you will need to use the chain rule twice. Each
    additional composite function within a function will require an additional chain rule.

  • Notice that the exponent is the outside of this expression. Next is the sine function. The argument of the sine function is the final function.

  • Here two functions are combined by multiplication. In addition, the second function is a composite function. To find the derivative you will need the product rule and the chain rule.

  • Start with the product rule. Remember that you will need to use the chain rule when asked to find the derivative of the second piece of the product.

  • This function is made up of the quotient of two other
    functions. Notice that none of these functions are composite functions.

  • Be careful when finding the derivative of the tangent
    function. If you do not remember the formula you can derive it by converting tangent to sines and cosines.

Calculate the slope of the line tangent to f (x) = 1 + e^2x at x = 0.

2

Find f′(x) if f(x)=cos(2x^2).

f′(x)=−4xsin(2x^2)

Suppose f(x)=2^(x^2−2x). Find f′(1).

f′(1)=0

Suppose f(x)=log_7x^2.What is the slope of the line tangent to f where x=2?

m=1/ln7

Use the definition of the derivative to evaluate the limit limh→0 ln(h+1)/h

lim h→0 ln(h+1)/h=1

Let f(x)=1−x^2+3x/2x^4. Rather than use the quotient rule to find f′(x), divide the denominator into the numerator first, and then find f′(x).

f′(x)=2x^2−9x−4/2x^5