Calculus 1 Hour Exam 2 - Math 220 Spring, 2010

1.	Evaluate the following derivatives: a. d/dx (csc x) b. d/dx (cot x) c. d/dx (sin^-1 x) d. d/dx( tan^-1 x) e. d/dx( 3^x ) Answers: a. – cscx cot x b. –csc^2 x c. 1/ √(1 – x^2) d. 1/(1+ x^2 ) e. 3^x ln 3
2.	Find g’(t) given that g(t) = 5t^3 - 3t^2 + 15 t - 18 Answer: g ‘(t) = 15 t^2 – 6t + 15
3.	Find f ‘ (x) given that f(x) = tan x / x^3 Answer: df/dx = ( x^3 sec^2x - 3 x^2 tan x ) / x^6
4.	Find P ‘ (t) given that P(t) = sin ( t^8 – 10t^2 + 5 ) Answer: dP/dt = (8 t^2 – 20 t) cos ( t^8 – 10 t^2 + 5 )
5.	Find dy/dx given that y = x ^ln^x Answer: dy/dx = ( x^ln^x ) [ 2 ln x / x ]
6.	Find dy/dx given that x^2 y^3 = 20x + 6y Answer: dy/dx = ( 20 – 2xy^3 ) / ( 3x^2y^2 – 6 )
7.	The graph of a function y = f(x) has the property that the slope of the tangent line at each point on the graph is equal to one half of its y-coordinate. If the graph goes through the point (0,6), then find a formula for f(x) . Answer: y = 6 e ^0.5x Click here to continue with this exam.

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