Question

Find the gradient of the scalar field
ϕ=xy2z3

y2z3i+2xyz3j+3xy2z2k

y2z3i+2xy2z3j+3xy2z3k

y2z3i+xyz3j+xy2z2k

y2z3+2xyz3+3xy2z2

Answer 1

Answer on Question #56118 – Math – Vector Calculus

Question

Find the gradient of the scalar field $\varphi = xy^2 z^3$.

Solution

$$grad\varphi = \frac{\partial\varphi}{\partial x}i + \frac{\partial\varphi}{\partial y}j + \frac{\partial\varphi}{\partial z}k = y^2z^3i + 2xyz^3j + 3xy^2z^2k.$$

Answer. $y^2z^3i + 2xyz^3j + 3xy^2z^2k$.

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