Let f(t) = ∛t . For a ≠ 0, find f ′(a)

Question

Let f(t) = ∛t . For a ≠ 0, find f ′(a)

Answer 1

Rewrite the function as:

Then apply the power rule (bring the exponent out front and reduce the exponent by 1 from what it was):

Then plug in "a":

Answer 2

Hey All, I would be happy to help you. Firstly it will be helpful to put this into exponential form, so we get f(t)=t^1/3. From here we simply follow the power rule (pull exponent out front to get coefficient and subtract one from the exponent) to get f'(t)=1/3t^-2/3. This can be rearranged to 1/3∛t² (the exponent is supposed to be under the radical). At this point we simply plug a in for t in f'(t) to get 1/3∛a². This is now solved, notice that since a is on the bottom of the denominator that is why a can not equal 0. Let me know if you have any questions or concerns.

Answer 3

f(t) = ³√t = t^1/3

So, f'(t) = (1/3)t^-2/3