Originally Posted by

**kingsolomonsgrave** I have a question about implicit differentiation.

In the case of differentiating the expression x^3+y^3=6xy the right hand side becomes 6xy'+6y where y is regarded as a function of x.

using the product rule $\displaystyle f'g+g'f $

$\displaystyle f = 6x$

$\displaystyle g = y$

then

$\displaystyle (6x)' y + 6y'$

so I get $\displaystyle 6y+6y'$

which is wrong.

Why is the right hand side equal to $\displaystyle 6xy'+6y$?

I (think) I know the key is that y is a function of x but somehow its not clicking as to why the answer is as it is.