Calculus 1 Hour Exam 2 - Math 220 Fall, 2010

1.	Evaluate the following derivatives. a. d/dx (cos x) b. d/dx (csc x) c. d/dx (tan x) d. d/dx (sin^-1 x) e. d/dx (ln x) Answers: a. – sin x b. – csc x cot x c. sec^2 x d. 1 / √ (1 – x^2 ) e. 1/x
2.	Find g ‘ (t) given that g(t) = 5t^5 + √t - 40 Answer: dg/dt = 25 t^4 + 1 / 2√t
3.	Find f ‘ (x) given that f (x) = x^5 / sin x Answer: df/dx = ( 5x^4 sin x - x^5 cos x ) / sin^2 x
4.	Find P ‘ (t) given that P(t) = ( t^9 - 10t^4 + 12 )^8 Answer: dP/dt = 8 (( t^9 - 10t^4 + 12 )^7 ( 9 t^8 – 40 t^3 )
5.	Find dy/dx given that x^5 e^y = 2x^3 + 5y^2 + 6 It is ok to leave your answer in terms of both x and y. Answer: dy/dx = ( 6x^2 – 5x^4 e^y ) / (x^5 e^y - 10y ) Click here to continue with this exam.

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