Pset4Answers - Ec115 Problem Set 4 The rules of dierentiation 1 Find the rst derivates of the following functions dy(i y = 3 2x dx = 2 dy y = c 2x

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Ec115 Problem Set 4. The rules of di/erentiation. (i) y = 3 + 2 x ) dy dx = 2 y = c + 2 x ) dy dx = 2 y = c + 2 x + bx 2 ) dy dx = 2 + 2 bx . (ii) Using the product rule: y = x (1 + x ) ) dy dx = (1 + x ) + x (1) = 1 + 2 x y = x (1 + 2 x 2 ) ) dy dx = (1 + 2 x 2 ) + x (4 x ) = 1 + 6 x 2 ; y = (1 + x + 2 x 2 )(1 3 x 3 ) ) dy dx = (1 + 4 x )(1 3 x 3 ) + (1 + x + 2 x 2 )( 9 x 2 ) : (iii) y = 1 x 1 ) dy dx = 1 x 2 ; y = x 1 (1 x ) = ) ( product rule) dy dx = ( x 2 )(1 x )+ x 1 ( 1) = x 2 = 1 x 2 . y = 1 x x ) ( quotient rule) dy dx = x ( 1) (1 x )(1) x 2 = x (1 x ) x 2 = 1 x 2 : (iv) y = x 1+ x ) ( quotient rule ) dy dx = (1+ x )(1) x (1) (1+ x ) 2 = 1 (1+ x ) 2 : y = x 2 1+ x ) ( quotient rule ) dy dx = (1+ x )2 x x 2 (1) (1+ x ) 2 = 2 x +2 x 2 x 2 (1+ x ) 2 = x (2+ x ) (1+ x ) 2 : (v) y = (1 + 2 x ) 3 ) ( Chain rule ) dy dx = 3(1 + 2 x ) 2 (2) = 6(1 + 2 x ) 2 y = (1 + 2 x 2 ) 3 ) ( Chain rule
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This note was uploaded on 12/31/2011 for the course ECON MR 102 taught by Professor Huyduong during the Winter '11 term at RMIT Vietnam.

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Pset4Answers - Ec115 Problem Set 4 The rules of dierentiation 1 Find the rst derivates of the following functions dy(i y = 3 2x dx = 2 dy y = c 2x

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