Question

How do you differentiate `f(x)=(x^2+e^x)/(x-1)^2` using the quotient rule?

Answer 1

`d/dx (x^2+e^x)/(x-1)^2=((x-1)^2*(2x+e^x)-2(x-1)*(x^2+e^x))/((x-1)^2)`

Explanation:

The quotient rule states that
`d/dxf(x)/(g(x))=(g(x)*f'(x)-f(x)*g'(x))/(g(x))^2`

So in this case,

`d/dx (x^2+e^x)/(x-1)^2=((x-1)^2*(2x+e^x)-2(x-1)*(x^2+e^x))/((x-1)^2)`