Anyone know calculus? What is the derivative of this?

[TheDude]

Hi all,

I was working on my math homework and I came across a problem that wanted me to find the derivative of this: X^3√(x+1)

Written out that is x cubed multiplied by the square root of x plus one. I can do the calculus part of the problem, but I cannot simplify it algebraically. Anyone want to help out?

Thanks!

 

[Homme]

Working on it, there doesn't look like there'll be a nice and neat solution.

I got [((x^2)/3)*√(x+1)]*(2x^2 + 2x + 9). Second half can't be factorised, unless you want the complex roots.

 

[TheDude]

whoa, how did you come to that? maybe I was unclear, it is x cubed as in x^3? could you maybe outline your steps?

 

[TKDKid]

I'm a bit rusty at this, but I get:

y = x^3 (x + 1)^(1/2)

dy/dx

= x^3 (1/2) (x + 1)^(-1/2) + 3x^2 (x + 1)^(1/2)

= (x^3) / [2(x + 1)^(1/2)] + 3x^2 (x + 1)^(1/2)

= [x^3 + 6x^2 (x + 1)] / [2(x + 1)^(1/2)]

= x^2 (7x + 6) / [2(x + 1)^(1/2)]

Hope that makes sense...?

 

[Homme]

Edit, was adding one to index instead of subtracting

. Seems i no longer know my derivatives from my integrals.

 

[TheDude]

hmm, this is what i get when I do it:

(3x^2)(√(x+1) ) + [(0.5(x+1)^(-0.5))(x^3)]

(3x^2(√(x+1))) + (x^3)/(2)(√(x+1))

And I don't know how to simplify further

 

[Homme]

Multiply your left term by (2√(x+1)) / (2√(x+1)); then add the two terms together.

 

[TheDude]

ah! there it is. I completely forgot about common denominators, lol. Thanks a bunch everyone!

 

[tiecollector]

I'm still confused, is it X^(3*√(x+1)) or is it (X^3) * (√(x+1)). Anyways, looks like two ppl got the same answer, haha, can't believe we are doing math problems on SF.

And I just did it myself and get the same answer as TKD and Homme.

 

[TheDude]

it is (X^3) * (√(x+1)) and that is most likely correct, since that is what I got as well.