Exam 2 Supplemental Problems Words of Advice Here are few things to keep in

# Exam 2 supplemental problems words of advice here are

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MAT 136: Calculus I Exam 2 Supplemental Problems Implicit Differentiation Use implicit differentiation to calculate dy dx for the following implicitly defined functions. 22. xy = 1 + x 2 y 23. cos( x - y ) = y sin( x ) 24. x 3 + x 2 y + 4 y 2 = 6 25. x 2 sin( y ) = ln( xy ) Logarithmic Differentiation 26. Use logarithmic differentiation to show that d dx [ x x ] = x x (ln( x ) + 1) 27. Use logarithmic differentiation to find the derivative of f ( x ) = ( x + 2) 2 e 100+ x 3 sin 7 ( x ) . Proofs 28. Prove the Product Rule using the limit definition of the derivative. 29. Prove that d dx [sin( x )] = cos( x ) using the limit definition of the derivative.

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