Exam 2 (B)

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Next: About this document MATH 1300.03F D Exam 2 Monday, November, 8 1999 NAME: Student Number: No. Marks (4 Marks) Find the derivative of each of the following functions. (1) . Solution: . (2) . Solution: f'(x)=-sin(5x+3)(5x+3)'=-5sin(5x+3). (3) f(x)=sec 2 (x+1) Solution: f'(x)=2sec(x+1)(sec(x+1))'=2sec(x+1)tan(x+1)sec(x+1)=2sec 2 (x+1)tan(x+1). (4) f(x)=cot 4 (5x 2 -2) . Solution: f'(x)= 4 cot 3 (5x 2 -2)[cot(5x 2 -2]' = 4 cot3(5x 2 -2)[ -csc2(5x 2 -2)(5x 2 -2)'] = -4 cot 3 (5x 2 -2)csc 2 (5x 2 -2).10x= -40x cot 3 (5x 2 -2)csc 2 (5x 2 -2). 2 (3 Marks ) Find the second derivative of the following implicitly defined function . Solution: Taking the derivative of this equation relative to x, we have 6x 2 +3y 2 y'=0 Hence, y'=-2x 2 /y 2 . Taking the derivative of ( 1 ), we obtain

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This implies 3 (8 Marks ) Let f(x)=x 2 /1+x. (1) Find the domain of f. (2) Find all the critical points of f and the second derivative of f. (3)
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