Question

Implicit derivative of y^3-xy=6
I know it's 3y^2 *dy/dx ----=0

Answer 1

yeah the first part is right
for the second part you need the product rule because you have a product
think of it as taking the derivative of \(-xf(x)\)
by the product rule you get \(-f(x)-xf'(x)\)

Answer 2

but instead of \(f(x)\) you write \(y\) and instead of \(f'(x)\) you write \(y'\) giving
\[3y^2y'-y-xy'=0\]

Answer 3

then a bit of algebra to solve for \(y'\) and that is the end

Answer 4

Alright thanks, that's exactly what i did