Try another version of this question Use logarithmic differentiation to find `dy/dx` if `y=(x+6)^(x-3)`. `dy/dx=`
Get help: Box 1: Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
To use logarithmic differentiation for `y = (x+6)^{(x+-3)}`, 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.
Be sure your variables match those in the question `(x+6)^(x-3)(ln(x+6)+(x-3)/(x+6))`