How do you use the quotient rule to differentiate #y=1/(x-4)^2#?
1 Answer
Mar 4, 2016
Explanation:
differentiate using the
#color(blue)" Quotient rule "# If
#f(x)=g(x)/(h(x)) "then " f'(x) =(h(x)g'(x) - g(x)h'(x))/(h(x))^2 # g(x) = 1
#rArr g'(x) = 0 # and
#h(x) = (x-4)^2 rArr h'(x) = 2(x-4) d/dx(x-4)# Replace these results into f'(x) :
#rArr f'(x) =( (x-4)^2 . 0 - 1 . 2(x-4))/((x-4)^2)^2#
# =( -2(x-4))/(x-4)^4 =-2(cancel(x-4))/(cancel(x-4))^3#
