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Clicker Question 1

Clicker Question 1. What is the instantaneous rate of change of f ( x ) = x 2 ln( x ) at x = e ? A. 2 B. 2e C. 3 D. 3e E. x (1 + 2 ln( x )). Clicker Question 2. What is the derivative of f ( x ) = (log 2 ( x )) 11/8 ? A. (11/8)(log 2 ( x )) 3/8

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Clicker Question 1

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  1. Clicker Question 1 • What is the instantaneous rate of change of f (x ) = x 2 ln(x ) at x = e ? • A. 2 • B. 2e • C. 3 • D. 3e • E. x (1 + 2 ln(x ))

  2. Clicker Question 2 • What is the derivative of f (x ) = (log2(x ))11/8 ? • A. (11/8)(log2(x ))3/8 • B. (11/8)(log2(x ))3/8 / (x ln(2)) • C. (11/8)(log2(x ))3/8 / x • D. (11/8)(log2(x ))3/8 ln(2) / x • E. (11/8)(1 / (x ln(2)))3/8

  3. Derivatives of Inverse Trig Functions (2/1/12) • We can use this same technique to discover the derivative formulas of inverse trig functions. • Apply implicit differentiation to both sides of the equation sin(y ) = x to discover the derivative of the arcsin. • Do the same for the arctan.

  4. Clicker Question 3 • What is the derivative of f (x ) = arcsin(x2) ? • A. 1 / (1 – x 2) • B. 1 /(1 – x 4) • C. arccos(x2) • D. 2x arccos(x2) • E. 2x /(1 – x 4)

  5. Now we have it all… • With the addition of these facts about derivatives of inverse functions, we now have (almost) all the information we need (i.e., all the “rules” and “facts”) to find the derivative of any combination of standard functions given by formula. • The only missing piece is a power function where the exponent is irrational.

  6. Assignment for Friday • On Page 217, do Exercises 49, 50, 51, 53, and 63. • Do the following problem:a. Sketch y = arcsin(x ) (Recall: domain is [-1,1])b. What is the slope of this function at x = 0?c. For what x ‘s is the slope 2? What is y at those points?

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