Question

As soon as I think I've finished, more work appears! YAY! (EXTREME sarcasm). I'll give a medal to anyone who can help me with the problem I'm posting below. :)

Answer 1

\[(x^2-1)^\frac{5}{2} (x^3+5)\]

Answer 2

what are the instructions?

Answer 3

Sorry, the directions are to find the derivative. (not sure why i didn't post that?)

Answer 4

So far I've gotten...

Answer 5

\[\:\left(x^2-1\right)^{\frac{5}{2}}\left(3x^2\right)+\left(x^3+5\right)\left(\frac{5}{2}\right)\left(x^2-1\right)^{\frac{3}{2}}\left(2x\right)\]

Answer 6

it looks great

Answer 7

I'm not exactly sure what I should do next. Should I begin to simplify or is there another step involved?

Answer 8

there's not much to simplify after this point

Answer 9

So that's it?

Answer 10

the only thing I can see really is factoring but it's not much of a simplification if you ask me

Answer 11

My teacher prefers specifics unfortunately. Could you help me identify what parts should be factored?

Answer 12

notice there's a x^2-1 repeated

Answer 13

\[\large \left(x^2-1\right)^{\frac{5}{2}}\left(3x^2\right)+\left(x^3+5\right)\left(\frac{5}{2}\right)\left(x^2-1\right)^{\frac{3}{2}}\left(2x\right)\]
\[\large \color{red}{\left(x^2-1\right)}^{\frac{5}{2}}\left(3x^2\right)+\left(x^3+5\right)\left(\frac{5}{2}\right)\color{red}{\left(x^2-1\right)}^{\frac{3}{2}}\left(2x\right)\]

Answer 14

Factor it out to get
\[\large \color{red}{\left(x^2-1\right)}^{\frac{5}{2}}\left(3x^2\right)+\left(x^3+5\right)\left(\frac{5}{2}\right)\color{red}{\left(x^2-1\right)}^{\frac{3}{2}}\left(2x\right)\]
\[\large \color{red}{\left(x^2-1\right)}^{\frac{3}{2}}\left(\left(x^2-1\right)\left(3x^2\right)+\left(x^3+5\right)\left(\frac{5}{2}\right)\left(2x\right)\right)\]
as you can see, it's not much of a simplification

Answer 15

well now that I think about it more, the 5/2 and 2x multiply to 5x

so that's something

Answer 16

Question: How come the 3/2 exponent was kept but not the 5/2 ?

Answer 17

I factored out the portion with the 3/2 exponent