If x^2y-3x=y^3-3, then at the point (-1,2), (dy/dx)?

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_______________

          dy
Find  ——  for an implicit function:
          dx

x²y – 3x = y³ – 3

First, differentiate implicitly both sides with respect to x. Keep in mind that y is not just a variable, but it is also a function of x, so you have to use the chain rule there:



Applying the product rule for the first term at the left-hand side:



                        dy
Now, isolate  ——  in the equation above:
                        dx





Compute the derivative value at the point (– 1, 2):

x = – 1   and   y = 2



I hope this helps. =)

Tags:  implicit function derivative implicit differentiation chain product rule differential integral calculus