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
Tuesday, September 4, 2018
ln(xy) + 5x = 30 Use implicit differentiation to find dy/dx
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