What is the Second Derivative Using Implicit Differentiation?

[superjen]

Use Implicit Differentiation to find y" if

xy + y - x = 1

so far i got

1y + dy/dx - dx/dx = 1/dx

then i did

y + y' - 1 = 0
y' = 1-y

i don't understand how to get the y" . i don't think i even have y' done right!

 

[gabbagabbahey]

Use Implicit Differentiation to find y" if

xy + y - x = 1

so far i got

1y + dy/dx - dx/dx = 1/dx

Careful; $$\frac{d}{dx}(xy)\neq y$$...you need to use the product rule.

And, $$\frac{d}{dx}(1)=0\neq\frac{1}{dx}$$

 

[jgens]

Perhaps to provide additional help, once you correctly find the first derivative, express it in terms of y' alone and then differentiate implicitly again.