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5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points. 5.3 Determining Intervals on Which a Function is Increasing or Decreasing. 5.4 Using the First Derivative Test to Determine Relative Local Extrema. 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema.
(7x2-1)2 3.1 The Chain Rule Calculus Find the derivative of each function. (3X2 — I. g(x) = Practice 5r2 — 2r 1 (loc -x) — In(2x3) 6. g(x) — 2. y sin 2x a: COS(xÒ • 5. h(x) = In(5X) cos x — cos (R
13) Give a function that requires three applications of the chain rule to differentiate. Then differentiate the function. Many answers: Ex y = ( ( ( 2 x + 1)5 + 2)6 + 3)7 dy = 7 ( ( ( 2 x + 1)5 + 2)6 + 3)6 ⋅ 6 ( ( 2 x + 1)5 + 2)5 ⋅ 5 ( 2 x + 1)4 ⋅ 2 dx. Create your own worksheets like this one with Infinite Calculus.
Composite Functions: Write your questions. 7. If 2 √1 find 3 . and thoughts here! 8. Given the following table of values, find ′. 4 for each function.
log(1 + x2) = d 1 = dxx2. dr log(2+sinr)Solution: x2 log(1 + x2) = Applying the product rule and then the chain rule we get: dx 2x log(1 + x2) + x2 1 1+x2 · 2x = 2x log(1 + x. ) + 2x3 1+x2 . Using the quotient rule and the ch. 1 = dr log(2 + sin r) 1 cos r log2(2 · · + sin r) 2 + sin r =. cos r :
Skill Builder: Topic 3.1 – The Chain Rule (Circuit) Begin in the first cell marked #1 and find the derivative of each given function. To advance in the circuit, search for your answer and mark that cell #2. Continue in this manner until you complete the circuit. Show all pertinent work.
A special rule, the chain rule, exists for differentiating a function of another function. This unit illustrates this rule. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature.
