Find the gradient of f (x,y,z) = x²y³z⁴ and f (x,y,z) = x²+y³+z⁴

Answer 1

For f(x,y,z) equal to x²y³z⁴, obtain: ∂f/∂x or 2y³z⁴x; ∂f/∂y or 3x²z⁴y²; and ∂f/∂z or 4x²y³z³.

The gradient of f(x,y,z) equal to x²y³z⁴ is then constructed as the vector (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k,

in this case equal to (2y³z⁴x)i + (3x²z⁴y²)j + (4x²y³z³)k.

For f(x,y,z) equal to x² + y³ + z⁴, obtain: ∂f/∂x or 2x; ∂f/∂y or 3y²; and ∂f/∂z or 4z³.

The gradient of f(x,y,z) equal to x² + y³ + z⁴ is then constructed as the vector (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k,

in this case equal to (2x)i + (3y²)j + (4z³)k.