Use logarithmic differentiation to find the following derivative:

Question

y=(x+6)^4/(x-5)^6. Please show all step so I can understand for future reference.

Answer 1

ln y = ln(x+6)^4 - ln(x-5)^6
ln y = 4ln(x+6) - 6ln(x-5)

y' / y = 4/(x+6) - 6/(x-5)

y' or dy/dx = y(4/(x+6) - 6/(x-5))
or
(x+6)^4/(x-5)^6 (4/(x+6) - 6/(x-5) )