Question

I dont understand where my mistake is. Can someone please help??! It involves derivatives.

Answer 1

I had to find the derivative of the original problem.

Answer 2

Did you try quotient rule?

Answer 3

Second step is wrong.

Answer 4

I used the product rule for the numerator and then I used the quotient rule for the simplified fraction.

Answer 5

What was wrong?

Answer 6

You can't just apply product rule for numeration while there is something not constant in denominator, you have to apply quotient right there.

Answer 7

multiply out the top, then use quotient rule

Answer 8

^

Answer 9

Oh okay. I'm gonna try that. So for future problems I can't combine different derivative rules in one problem?

Answer 10

well, roughly speaking, you shouldn't apply rule only to certain part of function, if you need to apply rule, you have to apply whole function.

Answer 11

I'm learning derivatives too, so I'm not an expert, but what I usually do is algebraically manipulate the function until I can use either a. a rule or b. a common derivative

Answer 12

softball if you want i can go over this problem with you on virtual whiteboard
it will be more convenient

Answer 13

thanks guys for helping! I tried redoing the problem, but I got stuck on one of the last steps.

Answer 14

do you still need help or are you done ?

Answer 15

the textbook says that the answer is 3/x^4

I can see that I came close to getting that answer, but I am stumped on what to do with the expression that is in the parenthesis on the numerator.

Answer 16

you're taking derivative wrong if i am not wrong. i don't understand what you did in line 4 of your picture

Answer 17

Third line, just simplify right there: \[\dfrac{x^3-1}{x^3}=\dfrac{x^3}{x^3}-\dfrac{1}{x^3} = 1-\dfrac{1}{x^3}\]

Answer 18

So then does that mean that \[1-\frac{ 1 }{ x^{3}}\] is the answer? Or do I have to continue using the quotient rule to finish it?

Answer 19

In first three lines, you just simplify the function, so taking derivative would be easier.
(y' in second and third line is supposed to be just y.)

So now you take derivative of \(1-\dfrac{1}{x^3}\)

Answer 20

OHHHHH I just got it!!!!!

Answer 21

OMG! The lightbulb just went off! LOL :)

Answer 22

Thanks so much for your help!! You are awesome! :)

Answer 23

Glad we helped!