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Use logarithmic differentiation to find `dy/dx` if `y=(x-3)^(x-2)`.
`dy/dx=`
To use logarithmic differentiation for `y = (x+-3)^{(x+-2)}`, start by taking the natural logarithm of both sides. This will allow you to use the properties of logarithms to simplify the expression. Then, differentiate both sides with respect to `x`, remembering to use the chain rule where necessary. Finally, solve for `dy/dx` by multiplying both sides by `y` and simplifying.
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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
`(x-3)^(x-2)(ln(x-3)+(x-2)/(x-3))`