If f(t)=(8t-(8/t))^(6/7)

then what is f'(t)?

Question

If f(t)=(8t-(8/t))^(6/7) 

then what is f'(t)?

calculusfunctions · Answer

You can apply the chain rule or you may first factor either the 8 or even 8/t and then apply product rule. Which would you be more comfortable doing?

anonymous · Answer

factor 8?

anonymous · Answer

8(t-8)^(6/7)

calculusfunctions · Answer

No. if you factor 8 from f(t) = (8t − 8/t)ˆ(6/7) then you get

f(t) = [8ˆ(6/7)](t − 1/t)ˆ(6/7)

You don't need the product rule here because 8ˆ(6/7) is a constant. Apply the power of a function rule.

f '(t) = (6/7)[8ˆ(6/7)][(t − 1/t)ˆ(6/7 − 1)][d(t − 1/t)/dt]

∴ f '(t) = (6/7)[8ˆ(6/7)][(t − 1/t)ˆ(-1/7)](1 + 1/t²).

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