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Unformatted text preview: 1 g ( x ) as ( g ( x ))-1 and using the product rule. (Ive tried to make this second method clear by rewriting the function for you in each case.) (a) f ( x ) = sin( x ) x 2 = sin x x-2 . (b) f ( x ) = x x 2 + x = ( x ) ( x 2 + x )-1 . 3. Compute the derivative of each of the functions below in two dierent ways. First use algebra (the binomial theorem) to expand the expression and apply a simple derivative formula. Then recompute the derivative by using the chain rule instead. (a) f ( x ) = ( x + 2) 3 . (b) f ( x ) = (3 x 2 + 1) 4 . Hints and Suggestions for Assignment 2 1. (a) Easy! (b) Write 3 x and 1 /x as powers of x . 2. (a) Straightforward. (b) Be willing to factor. 3. (a) Use Pascals triangle to write out ( A + B ) 3 . Here A = x and B = 2 so your answers will include powers of 2, like 4 or 8. (b) Use Pascals triangle to write out ( A + B ) 4 . Here A = 3 x 2 and B = 1....
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