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Katarina [22]
4 years ago
9

For the equation given below, evaluate y′ at the point (−2,2) xe^y−4y=2x−4−2e^2

Mathematics
1 answer:
jeka944 years ago
3 0
Implicit differentiation
chain rule is important here

I'll show the steps partially
e^y+xe^yy'-4y'=2
xe^yy'-4y'=2-e^y
y'(xe^y-4)=2-e^y
y'=\dfrac{2-e^y}{xe^y-4}
now evaluate for (-2,2)
x=-2 and y=2
y'=\dfrac{2-e^2}{-2e^2-4}
y'=\dfrac{2-e^2}{-2e^2-4}
y'=\dfrac{e^2-2}{2e^2+4}
that's it, simplest form
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