explain the steps used to find `dy/dx` using logarithmic differentiation; `root(9)((x-5)/(x+6))`
Logarithmic differentiation provides a way to differentiate a function possessing complicated exponents by taking logarithms first, and then by employing the logarithmic and other deriving techniques.
Taking log of both sides, note the properties of logarithms such that, `log(u/v)=logu-logv` and `log(u)^v=vlogu`
Differentiate both sides with respect to x, note that both side requires chain rule of differentiation,
Multiplying both sides by y such that y is eliminated from the L.H.S,
Therefore, logarithmic differentiation of the given function yields `dy/dx=11/(9*root(9)((x-5)^8(x+6)^10))`