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Find an equation of the tangent line to the following curve at point (0,4). xe^y+ye^x = 4.?

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  • Find an equation of the tangent line to the following curve at point (0,4). xe^y+ye^x = 4.?


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Answer #1 | 08/02 2014 12:51
tangent equation of f(x) at (a , f(a)) is y - f(a) = f '(a) (x - a)
Answer #2 | 08/02 2014 12:59
Differentiate implicitly. e^y + xe^y dy/dx + dy/dx e^x + ye^x = 0 ==> dy/dx = -(e^y + ye^x)/(xe^y + e^x). The slope m of the tangent line is dy/dx evaluated at (0, 4). m = -(e^4 + 4)/(1) = -(e^4 + 4). y - 4 = m(x- 0) ==> y = -(e^4 + 4)x + 4

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