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THE question 15. Compare the directional derivatived/ds at a point and in the di

ID: 2939318 • Letter: T

Question

THE question 15. Compare the directional derivatived/ds at a point and in the direction given by dz in the zplane, and the directional derivative of d/dS in thedirection of the w plane given by the image dw of dz. Henceshow that the rate of change of T in a given direction in the zplane is proportional to the corresponding rate of change of T inthe image direction of the w plane. Show that theproportionality constant is [dw/dz].
Can someone go through the steps required to prove this?
THE question 15. Compare the directional derivatived/ds at a point and in the direction given by dz in the zplane, and the directional derivative of d/dS in thedirection of the w plane given by the image dw of dz. Henceshow that the rate of change of T in a given direction in the zplane is proportional to the corresponding rate of change of T inthe image direction of the w plane. Show that theproportionality constant is [dw/dz].
Can someone go through the steps required to prove this?

Explanation / Answer

THE question 15. Compare the directional derivatived/ds at a point and in the direction given by dz in the zplane, and the directional derivative of d/dS in thedirection of the w plane given by the image dw of dz. Henceshow that the rate of change of T in a given direction in the zplane is proportional to the corresponding rate of change of T inthe image direction of the w plane. Show that theproportionality constant is [dw/dz].