)the purpose of this problem is to find the expression for the gradient in cylindrical coordinates. recall that in cartesian coordinates the gradient of a continuously differentiable function f(x, y, z) is ∇f = fx i + fy j + fz k. (1) recall also that the unit vector triads in the cartesian and cylindrical systems are related as follows. er = cos θ i + sin θ j, eθ = − sin θ i + cos θ j, ez = k. (2) i. use the above relations to show that i = er cos θ − eθ sin θ, j = er sin θ + eθ cos θ, k = ez.