ln(xy) + 5x = 30 Use implicit differentiation to find dy/dx

Find "dy"/"dx" if ln(xy)+5x=30 :
Use a property of logarithms to rewrite the first term:
lnx+lny+5x=30
Now differentiate term by term with respect to x:
1/x+1/y*(dy)/(dx)+5=0
1/y*(dy)/(dx)=-(1/x+5)
(dy)/(dx)=-y(1/x+5)
or (dy)/(dx)=-(y(1+5x))/x