Compute the gradient vector fields of the following functions: A. f(x,y)=1x2+7y2∇f(x,y)=i+j В. f(x,y)=x8y5,∇f(x,y)=□i+j C. f(x,y)=1x+7y∇f(x,y)=i+j D. f(x,y,z)=1x+7y+8z∇f(x,y)=i+j+k E. f(x,y,z)=1x2+7y2+8z2∇f(x,y,z)=i+j+k

Gradient of vector field f(x,y) is given by gradf(x,y)=(delf)/(delx)i+(delf)/(dely)j In partial derivative we find derivative of function wit...

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Pregunta: Compute the gradient vector fields of the following functions: A. f(x,y)=1x2+7y2∇f(x,y)=i+j В. f(x,y)=x8y5,∇f(x,y)=□i+j C. f(x,y)=1x+7y∇f(x,y)=i+j D. f(x,y,z)=1x+7y+8z∇f(x,y)=i+j+k E. f(x,y,z)=1x2+7y2+8z2∇f(x,y,z)=i+j+k
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Solución
Paso 1

Explanation:
Gradient of vector field f(x,y) is given by $\nabla f (x, y) = \frac{\partial f}{\partial x} i + \frac{\partial f}{\partial y} j$
In partial derivative we find derivative of function wit...
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Paso 2
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Texto de la transcripción de la imagen:

Compute the gradient vector fields of the following functions:

A. f (x, y) = 1 x^{2} + 7 y^{2} \nabla f (x, y) = i + j

В . f (x, y) = x^{8} y^{5}, \nabla f (x, y) = □ i + j

C. f (x, y) = 1 x + 7 y \nabla f (x, y) = i + j

D. f (x, y, z) = 1 x + 7 y + 8 z \nabla f (x, y) = i + j + k E. f (x, y, z) = 1 x^{2} + 7 y^{2} + 8 z^{2} \nabla f (x, y, z) = i + j + k