1. Find the derivative of the following functions. Simplify as much as possible. 1 a. f( x) = es 1 b. y = etex 1 c. y = sin(er) 3 y 2. Find the derivative of - + e = e. State the solution in the form _, where a and b contain only positive exponents. Simplify as much as possible. 3 3. Find the equation of the line tangent to the curve f(x) = e" at x = 2 in general form. 4. Determine the inverse of y = 31nL~r + 5}. Write the answer in the fen'n 3: =1" ' III}. 6. Rewrite each expression as a single logarithm. 1 a. Ina - Inb - 3 Inc 2 1 b. 5Inx + 2 In(x3 + 1)- 4In(x* -5) 7. Find the derivative of each of the following functions. Simply as much as possible. 1 a. f(x) = In(x -2) 1 b. y = Inx' + In 5