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)