题目
题目

PHAS0009_24-25 1.3 Quiz 1 [0.25 hrs]

单项选择题

The gradient ∇ϕ \nabla\phi of the scalar field ϕ(r)=x2+2xy+x2z2 \phi(\mathbf{r}) = x^2+2xy+x^2 z^2 is equal to

选项
A.2(x+y+xz^2)\,\hat{\mathbf{e}}_x+2y\,\hat{\mathbf{e}}_y + 2x^2 z\, \hat{\mathbf{e}}_z
B.2(x+y+xz)\,\hat{\mathbf{e}}_x+2x\,\hat{\mathbf{e}}_y + 2x^2 z\, \hat{\mathbf{e}}_z
C.2(x+y+xz^2)\,\hat{\mathbf{e}}_x+2x\,\hat{\mathbf{e}}_y + 2x^2 z\, \hat{\mathbf{e}}_z
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思路分析
The problem asks for the gradient ∇φ of the scalar field φ(r) = x^2 + 2xy + x^2 z^2. First, compute the partial derivatives with respect to each coordinate: - ∂φ/∂x: Differentiate x^2 with respect to x to get 2x; differentiate 2xy with respect to x to get 2y; differentiate x^2 z^2 with respect to x to get 2x z^2. Summing these gives ∂φ/∂x = 2x + 2y + 2x z^2 = 2(x + y + x z^2). - ......Login to view full explanation

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类似问题

Please select all the correct statements about the gradient.

Given the following function The gradient of f at (x,y) = (1,1) is

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Given the following function f(x,y)=3x2+y2+1 The gradient of f at (x,y) = (1,1) is

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