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Find an equation of the tangent line to the following curve at the point (0, 4).

xe^y+ye^x=4

1 answer

So one wants the line equation in the form of

y= dy/dx * x + b

from the original equation..
e^y + xe^y y' + y' e^x + y e^x=0

y' (xe^y+e^y)+ y e^x + e^y=0 check that.

I would put in (0,4) and solve for y' at this point.
Then go into the line equation
y=y' x + b and solve for b at 0,4
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