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Write the function `y=8/(x-6)^9` in the form `y=f(u)` and `u=g(x)`, then find `dy/dx` as a function of `x`.
`f(u)=`
`g(x)=`
Determine `dy/dx`.
`dy/dx=`
To approach this problem, focus on identifying the composite structure within the given function. Look for a way to separate the function into an outer function of `u` and an inner function of `x`. This separation will allow you to apply the chain rule effectively when finding `dy/dx`.
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Box 1: Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
Be sure your variables match those in the question
`8/u^9`
Box 2: Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
Be sure your variables match those in the question
`x-6`
Box 3: Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
Be sure your variables match those in the question
`-72/(x-6)^10`