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# hw9-14 - Assume k is another unknown function Try to guess...

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Math 170-010 Homework 9/14 Fall 2011 Goal: Use easy rules to compute derivatives. Recognize which rule applies to what kind of function. Here is the complete list of easy rules. Assume a , b and c are constants; f and g are functions. Function Derivative c 0 x 1 x n nx n 1 af + bg af + bg fg f g + fg f g f g - fg g 2 f ( g ( x )) f ( g ( x )) g ( x ) Exercises: From the Online Textbook, Section 3.5: Problems 1, 2, 3, 17, 19, 21, 22, 4, 5, 7, 6, 11, 36, 38, 39. Challenge Problems: 1. For each of these problems, assume that f , g and h are unknown functions of x . Find y and simplify as far as possible. (a) y = fgh (b) y = fg h (c) y = f gh (d) y = 1 fgh 1

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2. Did you simplify? Did you notice the patterns? Always one of each derivative. If there is a denominator, you get it back, squared. For each thing from the denominator, it’s derivative shows up negative.
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Unformatted text preview: Assume k is another unknown function. Try to guess the derivative of y = fg hk 3. The graphs of a function, f , and its derivative, f ′ , are shown at right. Suppose that g = x 2 f (a) Figure out which graph is f and which graph is f ′ . (b) Find g ′ (c) Estimate g ′ (2). 2 Hints and Answers Challenge 1. (a) y ′ = f ′ gh + fg ′ h + fgh ′ (b) y ′ = f ′ gh + fg ′ h-fgh ′ h 2 (c) y ′ = f ′ gh-fg ′ h-fgh ′ ( gh ) 2 (d) y ′ =-f ′ gh-fg ′ h-fgh ′ ( fgh ) 2 2. y ′ = f ′ ghk + fg ′ hk-fgh ′ k-fghk ′ ( hk ) 2 3. (a) Top graph is f , bottom is f ′ . (b) g ′ = 2 xf + x 2 f ′ . (c) g ′ (2) ≈ -60. 3...
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hw9-14 - Assume k is another unknown function Try to guess...

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