Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

ILet $f$ be of class $C^{(2)}$ and let $\displaystyle F(x,y)=f(x,xy)$, then I want to find the mixed partial derivative $\displaystyle F_{12}$.

Here I am letting $g^{1}(x,y)=x$ and $g^{2}(x,y)=xy$. Using the chain rule I get, $$F_{1}=f_{1}g_{1}^{1}+f_{2}g_{1}^{2}=f_{1}\cdot 1+f_{2}\cdot y.$$ Then I don't know how to find $F_{12}$? Please make a suggestion!

share|cite|improve this question
The sub/superscript notation used here is unnecessarily confusing. – JohnD Dec 16 '12 at 5:38

By $F_{12}$, do you mean $\displaystyle{{\partial^2 F\over \partial x\,\partial y}}$?

If so, take the partial with respect to $y$.

share|cite|improve this answer
Maybe, you mean $\dfrac{\partial^2{F}}{\partial{x}\partial{y}}$? – M. Strochyk Dec 16 '12 at 5:35
Thanks, misplaced ^2. Fixed now. – JohnD Dec 16 '12 at 5:36

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.