A. Give your own example of an equation containing the variables x and y and which cannot be solved for y. For this example, differentiate both sides implicitly. HINT: you might try an equation containing trig functions of both x and y, or an equation that contains several terms that feature powers of y.

B. We derived the definition of the derivative from the formula for the slope of a line. When we say that the derivative of a function is theslope of the line tangent to the functionat that point, what do we mean?

C. Let f(x) be a differentiable function of x. Give your own example of a function, f, for which it is necessary to use the Product Rule or Quotient Rule of differentiation.

D. Find the derivative of g(x) = sin(cos(Ln(3x))). What rule of differentiation did you need to use here? How many times did you have to use it? Was this problem difficult for you, or not so bad?