Question

how do i find the (d^2y)/(dx^2) for y=(x+2)/(x-3)

Answer 1

Let\[f(x)=\frac{x+2}{x-3}=(x+2)(x-3)^{-1}.\]Then\[f'(x)=(x+2)'(x-3)^{-1}+(x+2)[(x-3)^{-1}]'=(x-3)^{-1}-(x+2)(x-3)^{-2}\]\[=(x-3)^{-1}(1-(x+2)(x-3)^{-1}).\]You can do the second derivative.