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

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Answer 1 · 2018-06-02T16:15:35

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

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

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

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

$f’(x) = -3x^-2 - 5(1-x)^-2$

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

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