Thread: Implicit differentiation

Can someone spot my mistake, if there is one? Evaluate y' at the point (-1,2) if xe^y - 6y = 2x - 10 - e^2. Here's what I did: Taking the derivative of both sides, I got e^y + xe^y(y') - 6yy' = 2. Solving for y': y' = (2-e^y)/(xe^y - 6y). Putting in the values x=-1 and y = 2, I got: y' at that point = (2-e^2)/(-e^2-12). The computer homework system I'm using says this is incorrect. Did I make a mistake somewhere? Thanks for speedy help.

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[math] xe^y - 6y = 2x - 10 - e^2 [/tex]
Isolate constant terms:

Differentiate both sides:






y' =

You made a differentiation error on the 6y term. If f(y) = 6y,
then f'(y) = 6*(y'). If this were not implicit differentiation: if f(y)=6y,
f'(y) =6.

Thanks - I think I was needlessly employing the chain rule there.