Question

implicit differentiation
y = sin(7xy)
show steps please

Answer 1

\[y'=7\cos(7xy)\times(y+xy')\] is a start

Answer 2

only not obvious part is that the derivative of
\[xy\] requires the product rule, since you are thinking of y as a function of x. like taking the derivative of
\[xf(x)\] using the product rule. you would get
\[(xf(x))'=f(x)+xf'(x)\] but here you write
\[y+xy'\]

Answer 3

then algebra to solve for
\[y'\]

Answer 4

whats is wrong with this site, i am trying to post and answer and it freezes on me and then i have to refresh and i lose everthing i wrote

Answer 5

very very slow tonight

Answer 6

yeah its been slow for a couple of nights now