How do you differentiate $f (x) = \frac{1 - 4 x}{1 + 4 x}$ $f(x)=(1-4x)/(1+4x)$ using the quotient rule?

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Answer 1 · 2016-01-21T23:40:08

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

Given:

$f(x)=(g(x))/(h(x))$

$f'(x)=(g'(x)*h(x)-h'(x)*g(x))/(h^2(x))$

therefore:

$f'(x)=((0-4*1)(1+4x)-(1-4x)(0+4))/(1+4x)^2=$

$==(-4-cancel(16x)-4+cancel(16x))/(1+4x)^2=-8/(1+4x)^2$

How do you differentiate f(x)=(1-4x)/(1+4x)f(x)=1−4x1+4xf(x)=(1-4x)/(1+4x) using the quotient rule?