Help with a derivative and solving for Critical points

[LLofantaine]

I have the equation

(x^2)/(sqrt(x+1))

This one has been stumping me, not sure how to reduce the derivative properly much less solve for 0.

I get it down to this using the quotient rule:

((x+1)^(1/2)*2x - x^2*1/2(x+1)^(-1/2)) / (x+1)

Just started learning derivative a few weeks ago and they're still stumping me. I'm really terrible at simplifying these down. Once it's simplified down how would I solve for ZERO to find the crit points?

Any help would be appreciated.

 

[SammyS]

I have the equation

(x^2)/(sqrt(x+1))

This one has been stumping me, not sure how to reduce the derivative properly much less solve for 0.

I get it down to this using the quotient rule:

((x+1)^(1/2)*2x - x^2*1/2(x+1)^(-1/2)) / (x+1)

Just started learning derivative a few weeks ago and they're still stumping me. I'm really terrible at simplifying these down. Once it's simplified down how would I solve for ZERO to find the crit points?

Any help would be appreciated.

Hello LLofantaine. Welcome to PF !

The derivative is correct. The rest is just algebra.

((x+1)^(1/2)*2x - x^2*1/2(x+1)^(-1/2)) / (x+1) → $\displaystyle \frac{2x\sqrt{x+1}-\displaystyle \frac{x^2}{2\sqrt{x+1}}}{x+1}$

 

[LLofantaine]

Thanks, so that's what the derivative looks like, is there anyway to simplify that down further? Also, my algebra skills are obviously horrible so I can't remember the first thing about setting and solving that for 0

 

[SammyS]

Thanks, so that's what the derivative looks like, is there anyway to simplify that down further? Also, my algebra skills are obviously horrible so I can't remember the first thing about setting and solving that for 0

To reduce the fraction, multiply the "main" numerator & denominator by √(x+1) . That should allow you to simplify the numerator greatly.

(Yes. When students say they're having trouble doing the calculus, it's often the algebra skills that are lacking.)

 

[HallsofIvy]

The simplest way to handle this is NOT to use the quotient rule but, instead, write it as $$x^2(x+ 1)^{-1/2}$$ and use the product rule.