## anonymous 4 years ago Think my textbook may have the wrong answer for this: Find all higher derivatives -> f(r) = r(4r + 9)^3 I've tried a few different things, none are giving me the textbook answer. Please show explanation and not just the answer.

1. anonymous

I see you typing dumbcow. You're awesome :)

2. anonymous

this is combination of product rule and chain rule let u = r, v = (4r+9)^3 u' = 1 v' = 4*3(4r+9)^2 = 12(4r+9)^2 f'(r) = u'v + uv' f'(r) = (4r+9)^3 + 12r(4r+9)^2 ------------------------ for 2nd derivative let g(r) = 12r(4r+9)^2, we'll find g' first u = 12r, v = (4r+9)^2 u' = 12 v' = 4*2(4r+9) = 8(4r+9) g'(r) = u'v + uv' g'(r) = 12(4r+9)^2 + 96r(4r+9) --> f''(r) = 4*3(4r+9)^2 + 12(4r+9)^2 + 96r(4r+9) f''(r) = 24(4r+9)^2 + 384r^2 + 864r --------------------------- for 3rd derivative, f'''(r) = 48(4r+9) + 768r + 864 ----------------------------------- for 4th derivative f''''(r) = 192 + 768 = 960

3. anonymous

depending on how the textbook simplifies answers, it might be same thing but look different is everything expanded out in their answers?

4. anonymous

Here's the first two: $f \prime(r) = (16r+9)(4r+9)^{2}, f ^{n}(r) = 24(8r+9)(4r+9)$ It's strange because I went ahead and did the question after it and had no problems, although it is a slightly different question (4 sqrt(8x-3))

5. anonymous

Yeah I'm getting the same answer as you are, I'll leave a note asking my teacher to check it over himself before marking it.

6. anonymous

ok answers match, just checked the books are factored a little more nicely, thats all

7. anonymous

Okay thanks. I'm stuck in between 2nd and 3rd derivative, where you do f''(r) = 4*3(4r+9)^2 + 12(4r+9)^2 + 96r(4r+9), where is that first term coming from?

8. anonymous

for example: (4r+9)^3 + 12r(4r+9)^2 factor out a (4r+9)^2 (4r+9)^2(4r+9 +12r) =(16r+9) (4r+9)^2

9. anonymous

oh right sorry i was afraid of that, it comes from derivative of first term of f'(r) -->(4r+9)^3 + 12r(4r+9)^2 ^

10. anonymous

Hmm, I see how you got the first f"(r) of the second derivative, but not how you got the 24(4r+9)^2 in the second step. I'll continue this from school, in about 1:30 hours. Wish me luck!

11. anonymous

Ahh ...i just combined terms, 4*3=12 ...12+12 =24 good luck

12. anonymous

oh and then i expanded 96r(4r+9)