Question

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

Answer 1

`-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)`