Find the gradient vector field of the function $f ( x ; y ) = x + y ^ { 2 }$
A)$2 \mathrm { j }$
B)$\mathbf { i } + 2 \mathbf { j }$
C)$\mathbf { i } + 2 y \mathbf { j }$
D) $x \mathbf { i } + 2 y \mathbf { j }$
E)$- 2 j$
F)$- \mathbf { i } - 2 \mathbf { j }$
G) $- \mathbf { i } - 2 y \mathbf { j }$
H) $- x \mathbf { i } - 2 y \mathbf { j }$

Question

Find the gradient vector field of the function $f ( x ; y ) = x + y ^ { 2 }$ 
A)$2 \mathrm { j }$ 
B)$\mathbf { i } + 2 \mathbf { j }$ 
C)$\mathbf { i } + 2 y \mathbf { j }$ 
D) $x \mathbf { i } + 2 y \mathbf { j }$
E)$- 2 j$ 
F)$- \mathbf { i } - 2 \mathbf { j }$ 
G) $- \mathbf { i } - 2 y \mathbf { j }$ 
H) $- x \mathbf { i } - 2 y \mathbf { j }$

Quizplus · Accepted Answer

The gradient vector field of a function $f(x, y)$ is given by $\nabla f = \frac{\partial f}{\partial x} \mathbf{i} + \frac{\partial f}{\partial y} \mathbf{j}$. For $f(x, y) = x + y^2$, $\frac{\partial f}{\partial x} = 1$ and $\frac{\partial f}{\partial y} = 2y$, thus the gradient is $\mathbf{i} + 2y \mathbf{j}$.

Find the Gradient Vector Field of the Function f(x;y)=x+y2f ( x ; y ) = x + y ^ { 2 }f(x;y)=x+y2

Find the Gradient Vector Field of the Function $f ( x ; y ) = x + y ^ { 2 }$