12.

\f9-18. Chain Rule with one independent variable Use Theorem 15.7 to find the following derivatives.12. Directional derivatives Consider the function f (x, y) = 2x2 + 322, Whose graph is a paraboloid (see figure). \f(0,5) = (1,0) (125) = (1,1) (a,b) = (1,2) a. Fill in the table with the values of the directional derivative at the points (a, b) in the directions given by the unit vectors u, v, and W. b. Interpret each of the directional derivatives computed in part (a) at the point (1, O). 3136. Direction of steepest ascent and descent Consider the following functions and points P. a. Find the unit vectors that give the direction of steepest ascent and steepest descent at P. b. Find a vector that points in a direction of no change in the function at P. \fTheorem 15.7: Chain Rule (One Independent Variable) Let 2 be a differentiable function of x and 3/ on its domain, where x and y are differentiable functions of t on an interval I. Then