Question

How do you differentiate `f(x)=3/x-5/(1-x)` using the sum rule?

Answer 1

`color(maroon)(f’(x) = -(3/x^2 + 5/(1-x)^2)`

Explanation:

`f(x) = (3/x) - (5/(1-x))`

`f(x) = 3x^-1 - 5(1-x)^-1`

`f’(x) = (3 * -1* x^-2) - (5 * -1 (1-x)^-2 * -1)`

`f’(x) = -3x^-2 - 5(1-x)^-2`

`color(maroon)(f’(x) = -(3/x^2 + 5/(1-x)^2)`