Question

Find y' if 5y+8x^4=ln(6yx)

Answer 1

hint:
ln(6yx)=ln6+lny+lnx (multiplication rule of logarithms)
and
(ln y)'=d(lny)/dy*dy/dx=(1/y)y' (chain rule)

Answer 2

I see, but how do I isolate y? Because it would be 5y-lny=ln6+lnx-8x^4 and I need to find y'

Answer 3

You definitely need to isolate y', and y can be used in implicit derivatives unless specifically asked to have the derivative free of y. So don't need to isolate y before deriving.
Derive term by term, then isolate y'. The expression will be in terms of x and y and constants.

Answer 4

example:
xy^2+x^3=0
derive term by term:
y^2+2xyy'+3x^2=0
isolate y'
2xyy'=-y^2-3x^2
y'=-(y^2+3x^2)/(2xy)

Answer 5

ohhh ok, I'll try that