How do you find the derivative of #f(x)= 1/(x-7) #?

1 Answer
Jun 21, 2016

#-1/(x-7)^2# or #-1/(x^2-14x+49#

Explanation:

The quotient rule : # d/dx[f(x)/g(x)] = (f'(x)*g(x) - g'(x)*f(x))/(g(x))^2# where #f(x)# is the numerator and #g(x)# is the denominator

so plugging in our values:

#([d/dx1*(x-7)]-[d/dx(x-7) * 1])/(x-7)^2# #-># #([0*(x-7)]-[1*1])/(x-7)^2#

which simplifies to:
#-1/(x-7)^2#

also quick tip: the first derivative of #1/n# will always be #-1/n^2# as long as #n# is always #n^1# for basic functions like #1/(x-7)#