Homework SourseUse implicit differentiation to find the equation of the tan
Use implicit differentiation to find the equation of the tangent line to
the curve xe^(y)? ye^(x) = 1 at the point (0,1) DO NOT approximate
e in your final answer.
the curve xe^(y)? ye^(x) = 1 at the point (0,1) DO NOT approximate
e in your final answer.
Solution
Differentiate:
d/dx (xe^(y) ye^(x) = 1)
1*e^(y) + x.y\'.e^(y) - y\'e^(x) - ye^x = 0
y\'(x.e^y - e^x) = y.e^x - e^y
y\' = (y.e^x - e^y)/(x.e^y - e^x)
x = 0 , y = 1 :
y\' = (1*1 - e)/(0 - 1) = e - 1
