SOLUTION: Find x’ for the function x(t) defined implicitly below. Compute the equation of the tangent line at the indicated point. t ln x = xe^t-1 ; (t,x) = (0,1)

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Question 1088245: Find x’ for the function x(t) defined implicitly below. Compute the equation of the tangent line at the indicated point.
t ln x = xe^t-1 ; (t,x) = (0,1)
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!


Differentiating implicitly to find 



Clear the fraction by multiplying through by LCD=x









When y is the dependent variable and x is the independent
variable, the point-slope equation of the line through
(x1,y1) with slope m is .

But in this case, x is the dependent variable and t is the independent
variable, so the equation of the line through (t1,x1)
with slope m is .

(t1,x1) = (0,1)

And the slope m is x' evaluated at this point:






 
So 

So substituting m = -1, and (t1,x1) = (0,1)









Edwin
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