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Question

If ex+ey=e(x+y), then dydxat(2,2) is


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Solution

Step 1 : Differentiating both sides with respect to x

Given that ex+ey=e(x+y)

ex+(ey)(dydx)=ex+y(1+dydx)exex+y=(dydx)(ex+yey)(dydx)=(ex+yex)(eyex+y)

Step 2 :Finding the value of dydxat(2,2):

dydx=(e2+2e2)(e2e2+2)=-(e2+2e2)(e2+2-e2)=-1

Hence, the value of dydxat(2,2) is -1.


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