Asked by Anonymous
Find the derivative of (3x+17)^13 (14x+6)^11x^-4/5 / (20x +3)^-9
using logarithmic differentiation. Assume x > 0.
Answers
Answered by
Steve
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.
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.
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