Find Düg(1, −1) where g(x, y) = e−(x²+y²) and u is the unit vector parallel to < 3, −4 >.

The cost to produce a certain product depends on 3 main variables, denoted p, q, and r. If C(p, q, r) = C₂e-2p + 7q − 9r represents the cost function, find the greatest rate of decrease of this function at the point Po(100, 51, 10). Cov 134 e 118 X Find the unit vector direction in which the greatest rate of decrease of the function occurs at Po. (Your instructors prefer angle bracket notation for vectors.) 118 Co√ 134 e¹ OV X

Find the directional derivative of f(x,y,z) = z3-x2y at the point (4, -3, 4) in the direction of the vector v = <-1,-3,-2>.

Find the derivative of the vector function r(t) tax (btc), where a = (2, -5,-2), b = (4, 2,-5), and c = (3,-2,-2). r' (t) = (