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How do you derive this?? 10 PTS...?
Now originally the function is (5u^7)/(((u^5)-1)^6)
Then I turn it into product rule so it becomes (5u^7)*(((u^5)-1)^-6) just to make it simpler...
I keep getting answers similar to the final answer but nope...never right on the spot
Answer is supposedly (-5u^6)*(((u^5)-1)^-7)*((23u^5)+7)
1 個解答
- No MythologyLv 71 十年前最愛解答
The answer you posted is correct.
d/du 5u^7(u^5 - 1)^(-6) = -30u^7(5u^4)(u^5 - 1)^(-7) + 35u^6(u^5 - 1)^(-6)
If you factor out the common 5u^6(u^5 - 1)^(-7), you can simplify this as
d/du 5u^7(u^5 - 1)^(-6) = 5u^6(u^5 - 1)^(-7)[ -30u^5 + 7(u^5 -1)]
= 5u^6(u^5 - 1)^(-7)(-23u^5 - 7).
Finally, pulling the last negative sign to the front gives
d/du 5u^7(u^5 - 1)^(-6) = - 5u^6(u^5 - 1)^(-7)(23u^5 +7).
I'm not convinced that turning the quotient into a product always makes these things easier. You can just as easily compute
d/du 5u^7/(u^5 - 1)^6 = 35u^6/(u^5 - 1)^6 - 6(5u^4)(5u^7)/(u^5 - 1)^7
= 35u^6/(u^5 - 1)^6 - 150u^11/(u^5 - 1)^7
