If f(x) = 1/(6x^2), where x not equal to 0, find the rate of change when x=4.

f(x) can be rearranged to be: f(x) = 1/6 x^-2This is then differentiated to be: f'(x) = -1/3 x^-3 as the expression is multiplied by the original power (-2) and then the power is reduced by 1 (to -3)
f'(x) is then rearranged to be f'(x) = -1/(3x³) which x=4 can then be substituted into giving:
f'(4) = -1/(3*4³) = -1/192