Question

Let
ϕ=2x^z^4−x^2y
,find
|▽ϕ|

5(√97)

3(√112)

(√105)

2(√93)

Answer 1

Answer on Question #56125 – Math – Vector Calculus

Let $\varphi = 2x^{\wedge}z^{\wedge}4 - x^{\wedge}2y$, find

$$|\nabla \varphi|$$

5(v97)

3(v112)

(v105)

2(v93)

Solution

$$\nabla \varphi = \left(\frac{\partial \varphi}{\partial x}, \frac{\partial \varphi}{\partial y}, \frac{\partial \varphi}{\partial z}\right) = \left(\frac{\partial (2xz^4 - x^2y)}{\partial x}, \frac{\partial (2xz^4 - x^2y)}{\partial y}, \frac{\partial (2xz^4 - x^2y)}{\partial z}\right) = (2z^4 - 2xy, -x^2, 8xz^3).$$ $$|\nabla \varphi| = \sqrt{(2z^4 - 2xy)^2 + (-x^2)^2 + (8xz^3)^2}.$$

If we need the number in the answer we need to choose a point $(x_0, y_0, z_0)$ where we calculate $|\nabla \varphi|$.

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