Suppose that f(x) and g(x,y) are functions. What is the partial derivative of f(g(x,y)) with respect to y?

Find the roots, if they exist in the real numbers, of the quadratic equation

The first derivative of a function f(x) is zero at some point, the second derivative is also zero at this point. This means that:

You are given the following regressions of the first difference of the log of a commodity price on the lagged price and of the first difference of the log return on the lagged log return. Each regression is based on 100 data points and figures in square brackets denote the estimated standard errors of the coefficient estimates:
Which of the following hypotheses can be accepted based on these regressions at the 5% confidence level (corresponding to a critical value of the Dickey Fuller test statistic of - 2.89)?

An asset price S is lognormally distributed if: