Differentiate f(x) = 1/(x + 7)

Use the quotient rule:

If f(x) = u/v, then f'(x) = (u'v - uv') / v^2

So,

f(x) = 1/(x+7)

f'(x) = ((1)'(x+7) - 1(x+7)') / (x+7)^2

f'(x) = (0*(x+7) - 1(1)) / (x+7)^2

f'(x) = -1 / (x+7)^2