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Gradient Determination of Functions

Calculate the gradient Vf of the following functions, f(x,y,z)
a. f = x^2 + z^3
b. f = ky where k is a constant
c. f = r = (x^2 + y^2 + z^2)^1/2 Hint use the chain rule
d. f = 1/r

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This solution contains step-by-step calculations to determine the gradient of the vector operator using cross product and chain rule.