How do you differentiate $f(x) = (3 + 4x)/(1 + x^2)$ ?

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Answer 1 · 2015-06-02T00:45:55

The quotient rule, which we'll use here, states that, be $y=f(x)/g(x)$ , then $y'=(f'(x)g(x)-f(x)g'(x))/(g(x)^2)$ .

Thus,

$y'=(4*(1+x^2)-(3+4x)*2x)/(1+x^2)^2$

$y'=(4+4x^2-6x-8x^2)/(1+x^2)^2$

$y'=(-4x^2-6x+4)/(1+x^2)^2$

How do you differentiate f(x) = (3 + 4x)/(1 + x^2)f(x) = (3 + 4x)/(1 + x^2)?