Given e^-xy - 4xy=0, dy/dx can be proved as
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65
Given, e^{-xy} - 4xy = 0
difference with respect to x
e^{-xy}[d(-xy)/dx ] - 4[ydx/dx + xdy/dx ] = 0
e^{-xy}[ -ydx/dx - xdy/dx] - 4[y + xy'] = 0 [ ∵ dy/dx = y' ]
e^{-xy}[-y - xy'] - 4[y + xy'] = 0
[y + xy'][e^{-xy} + 4] = 0
y + xy' = 0 because e^{-xy} + 4 ≠ 0
y' = -y/x
Hence, dy/dx = -y/x
difference with respect to x
e^{-xy}[d(-xy)/dx ] - 4[ydx/dx + xdy/dx ] = 0
e^{-xy}[ -ydx/dx - xdy/dx] - 4[y + xy'] = 0 [ ∵ dy/dx = y' ]
e^{-xy}[-y - xy'] - 4[y + xy'] = 0
[y + xy'][e^{-xy} + 4] = 0
y + xy' = 0 because e^{-xy} + 4 ≠ 0
y' = -y/x
Hence, dy/dx = -y/x
Answered by
3
Step-by-step explanation:
Take the derivative of e^-xy - 4xy = 0
Please see the image for remaining solution.
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