Question

How are the directional derivative and partial derivative related (more information in the image)

Assuming that the necessary derivatives of f(x,y,z) are defined, how are Dif, Dif, and Df related to f, fy, and f,? Give reasons for your answer.
Choose the correct answer below.
O A. D,f, D,f, and Df are equal to fy, fy, and f, respectively, because when u i, the directional derivative at Po is f, evaluated at that point, when u j, the directional derivative at Po is f, evaluated at that point,
when u k, the directional derivative at Po is f, evaluated at that point
0
X
O B. D,f, D,f, and Df are not related to fy, fv, and f,.
O C. D,f, D,f, and Df represent the rate of change in the same direction as fy, f, and f, respectively, because directional vectors and gradient vectors have the same direction.
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Transcribed Image Text:Assuming that the necessary derivatives of f(x,y,z) are defined, how are Dif, Dif, and Df related to f, fy, and f,? Give reasons for your answer. Choose the correct answer below. O A. D,f, D,f, and Df are equal to fy, fy, and f, respectively, because when u i, the directional derivative at Po is f, evaluated at that point, when u j, the directional derivative at Po is f, evaluated at that point, when u k, the directional derivative at Po is f, evaluated at that point 0 X O B. D,f, D,f, and Df are not related to fy, fv, and f,. O C. D,f, D,f, and Df represent the rate of change in the same direction as fy, f, and f, respectively, because directional vectors and gradient vectors have the same direction.
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