Question

Use implicit differentiation to find dy/dx.
ln xy + 5x = 30. Please write out the steps.

Answer 1

you need to use chain rule for ln(xy)
and then product rule for xy.
try it. if you can't get, i'll help you further.

Answer 2

d/dx (ln xy +5x) =d/dx (30)
d/dx (ln xy) + d/dx (5x) =0
d/d(xy) (lnxy) * d/dx(xy) +5=0
1/xy * { d/dx(x) *y + x * d/dx(y)}=-5
y+x *dy/dx =-5xy
x*dy/dx =-5xy-y
dy/dx = -(5xy+y)/x