Find the gradients of the following functions: (a) f (x, y, z) = x2 + y3 + z4. (b)

Question

Find the gradients of the following functions:

(a) f (x, y, z) = x2 + y3 + z4.

(b)

Answer 1

The gradient is df/dx i + df/dy j + df/dz k where the ds are partial derivatives and the i,j,k are the coordinate unit vectors.

2x i + 3y² j + 4z³ k

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