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Solve this function for its derivative using the quotient rule.

f(t) = (3^(1/2))/t^3

I used the quotient rule by taking the denominator and multiplying it by the derivative of the numerator and subtracting that quantity by the sum of the numerator and the derivative of the denominator and then placing that whole quantity over the denominator squared. I get to this point and then don't know how to properly simplify what I have derived.

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  • $\begingroup$ Are you perhaps missing a $t$ in the numerator? Otherwise the numerator is constant and you wouldn't need quotient rule to differentiate, since $3^{1/2}/t^3 = 3^{1/2}t^{-3}$ and you can use power rule. $\endgroup$ – minimalrho Oct 8 '14 at 0:34
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Or, you can simplify the function as follows: $$f(t) = \frac{3^{1/2}}{t^3} = \sqrt{3}\,t^{-3},$$ so that $$f'(t) = -3\sqrt{3}t^{-4} = -\frac{3\sqrt{3}}{t^4}.$$

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