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133exam1xsolution

# 133exam1xsolution - Math 133 Dr Kurtz Exam 1 Name Section...

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Math 133 Exam 1 Name___________________ Dr. Kurtz Section No.______________ TA_____________________ Instructions : Please show all of your work. Credit will not be given for answers with no supporting work. 1. (21 pts) Compute dy dx . (a) 2 1 cos x y e x = 2 2 2 1 1 ( 2 )cos sin x x y e x e 1 x x x ⎞⎛ ′ = ⎟⎜ ⎠⎝ (b) tan(ln( )) y = x or equivalently, 1 tan ln 2 y x = 2 1 1 sec (ln( )) 2 y x x x ⎞⎛ ′ = ⎟⎜ ⎠⎝ or equivalently, 2 1 1 sec ln 2 2 y x x ⎞⎛ ′ = ⎟⎜ ⎠⎝ (c) sin (ln ) x y x = ln sin ln(ln ) y x x = 1 1 cos ln(ln ) sin ln y x x x y x x = + sin 1 1 (ln ) cos ln(ln ) sin ln x y x x x x x x ′ = + Alternatively, sin ln(ln ) x x y e = sin ln(ln ) sin 1 1 1 1 cos ln(ln ) sin x x (ln ) cos ln(ln ) sin ln ln x x x y e x x x x x x x x x = + = +

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