How do you differentiate #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#