SOLUTION: Please find derivative and simplify: y=ln(3x-5)^3/(5x+4)^4

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Question 59245: Please find derivative and simplify:
y=ln(3x-5)^3/(5x+4)^4
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Please find derivative and simplify:
d/dx[ln(x)]=1/x
d/dx[cf(x)]=cf'(x)
d/dx[c]=0
Chain Rule: d/dx[f(g(x))]=f'(g(x))*g'(x)
:
y=ln((3x-5)^3/(5x+4)^4) Use properties of logs to simplify first.
y=ln((3x-5)^3)-ln((5x+4)^4)
y=3ln(3x-5)-4ln(5x+4) Now take the derivative using the chain rule:
dy%2Fdx=3%281%2F%283x-5%29%29%283%29-4%281%2F%285x%2B4%29%29%285%29
highlight%28dy%2Fdx=9%2F%283x-5%29-20%2F%285x%2B4%29%29
Happy Calculating!!!