1.) Let y = f(x) = (x³ - 1)² = x⁶ - 2x³ + 1

a.) Find the derivative of y using f(x) = x⁶ - 2x³ + 1.

b.) Find the derivative of y using f(x) = (x³ - 1)² and the chain

rule (u substitution).

c.) D o your answers from (a) and (b) match? (yes or no)

2.) Find the derivatives of y for

a.) y = 2e^5x

b.) y = -2e^-4x

3.) Find the derivatives of y for

a.) y = sin(5x)

b.) y = 3tan(x²)

4.) Find the derivatives of y for

a.) y = 3sec(x⁴)

b.) y = 1/e^2x

5.) Find the derivative of y using logarithmic differentiation when y = x(x-2)²(2x-1)^-1

Note: There are different formats of the correct answer. If your format is not my format, how do I check your answer? I plot my answer and your answer and see if the two plots lie on top of each other!

6.) Let y = 3^x

a.) Let y = 3^x = e^ax

y = (3)^x = (e^a)^x

What is a?

b.) Find the derivative of y. Be sure you change any e^ax

back to 3^x.