Differentiate ((x - sqrt of x) / (x^1/9)) . I'll write the equation also from the equation box.

Question

kainui · Answer

If I were you I'd combine all the x's into one x using exponent rules and use the power rule to differentiate in one sweep!

kainui · Answer

Actually that's not exactly possible, but almost.

kainui · Answer

You can still simplify it down quite a bit with exponent rules, show me where you get stuck and I'll assist.

anonymous · Answer

$$\frac{ d }{ dx } (\frac{ x-\sqrt{x} }{ x^{1/9}})$$

anonymous · Answer

At first before i started to differentiate I rewrote it as $$\frac{ x^{1} }{ x^{1/9} } - \frac{ x^{1/2} }{ x^{1/9} }$$

kainui · Answer

Good, you're on the right track. You can simplify it further still before taking the derivative.

anonymous · Answer

Then I got $$x^{8/9} - x^{7/18}$$

kainui · Answer

Yep.

anonymous · Answer

Then i did the derivative of that and got $$\frac{ 8 }{ 9 }x^{-1/9} - \frac{ 7 }{ 18 }^{-11/18}$$

anonymous · Answer

Can you tell me if im doing smthg wrong. When i write that answer in my hw it marks it wrong

kainui · Answer

Absolutely correct.

kainui · Answer

Maybe your homework wants you to put it in a certain form.

kainui · Answer

It will look slightly different if you don't simplify it before evaluating it. Does it want you to find it using the quotient rule?

anonymous · Answer

I think it does. Thats how the last couple of problems were done.

kainui · Answer

That sucks, because once you get past calculus 1 you will probably never use the quotient rule ever again since every fraction can be rewritten in a form that looks like the product rule and is much simpler to do in my opinion.

All I can say is just follow the quotient rule template and do it. Your answer isn't wrong, they're just jerks about it.

kainui · Answer

Since you already worked it out this way, you might want to see if you can show that the quotient rule answer you found is equal to the simplified version you did to prove to yourself that they're equivalent statements.

anonymous · Answer

Ok thank you. As long as my asnwer is not incorrect thats all that matters now since im studying for finals and my proff will see my correct wrk anyways if a problem like this comes up. Thank you for confirming my answer.

kainui · Answer

Yeah, glad I could help. In my opinion the quotient rule should never be used because it can only mess you up while the product rule will never matter what order you do it in. Good luck on your final!