You can put this solution on YOUR website! the limit definition of the first derivative of a function is
f'(x) = (f(x+h) - f(x)) / h as h ---> 0
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we are given f(x) = 6 / x^2
:
we substitute x+h for x, then
:
f'(x) = ((6 / (x+h)^2) - (6 / x^2)) / h
:
f'(x) = (6x^2 - 6(x+h)^2) / (x^2 * (x+h)^2) / h
:
f'(x) = (6x^2 -6(x^2+2xh+h^2)) / (h(x^2 * (x^2+2xh+h^2)))
:
f'(x) = (6x^2 -6x^2 -12xh -6h^2) / (h * (x^4 +2x^3h +x^2h^2)
:
f'(x) = h(-12x -6h) / (h * (x^4 +2x^3h +x^2h^2))
:
f'(x) = (-12x -6h) / (x^4 +2x^3h +x^2h^2)
:
f'(x) = -12x / x^4 as h---->0
:
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f'(x) = -12 / x^3
