Expert: Ahmed Salami - 3/5/2010

Question
I am having trouble finding dy/dx by implicit differentiation in the equation x^2y^3-9xy^2=11. Can you help?

Answer
Hi Allison,
The trick is to always add dy/dx when you differentiate any term in y.
x²y³ - 9xy² = 11
Using product rule,
[x².3y²(dy/dx) + y³.2x] - [9x.2y(dy/dx) + y².9] = 0
3x²y²(dy/dx) + 2xy³ - 18xy(dy/dx) - 9y² = 0
3x²y²(dy/dx) - 18xy(dy/dx) = 9y² - 2xy³
(3x²y² - 18xy)(dy/dx) = 9y² - 2xy³
dy/dx = (9y² - 2xy³)/(3x²y² - 18xy)
     = y²(9 - 2xy)/3xy(xy - 6)
     = y(9 - 2xy)/3x(xy - 6)

Regards