Find the derivative of (3x+17)^13 (14x+6)^11x^-4/5 / (20x +3)^-9

Question

using logarithmic differentiation. Assume x > 0.

Answer 1

y = (3x+17)^13 (14x+6)^11x^-4/5 / (20x +3)^-9

ln y = 13ln(3x+17) + 11 ln(14x+6) - 4/5 ln(x) + 9ln(20x+3)

1/y y' = 39/(3x+7) + 154/(14x+6) - 4/(5x) + 180/(20x+3)

Now the rest is just algebra.

See if you get the result here:

http://www.wolframalpha.com/input/?i=(3x%2B17)%5E13+(14x%2B6)%5E11+x%5E(-4%2F5)+%2F+(20x+%2B3)%5E-9

scroll down some distance to get the derivative.