Derivative

[Loki123]

We have what y is (first line). We are supposed to calculate the expression under it (second line). It gets too complicated. Is there a trick?

 

[Steven G]

Keep going. You are on the right path.

 

[Loki123]

Keep going. You are on the right path.

I just get lost after applying the derivatives in the expression

 

[Steven G]

Simplify things, like no negative exponents.

 

[Deleted member 4993]

We have what y is (first line). We are supposed to calculate the expression under it (second line). It gets too complicated. Is there a trick? View attachment 32257

Now just use those y' and y" and evaluate the given expression. It is a dreary calculation but doable.

Do you have the expected answer?

 

[BigBeachBanana]

We have what y is (first line). We are supposed to calculate the expression under it (second line). It gets too complicated. Is there a trick? View attachment 32257

Let [imath]f(x)=x\quad \&\quad g(x)=\sqrt{x^2+1}[/imath]
[math] y=(f+g)^n\\ y'=n (f+g)^{n-1}(f'+g')\\ \tag{Product rule} y''=n(n-1)(f+g)^{n-2}(f'+g')(f'+g')+n (f+g)^{n-1}(f''+g'') [/math]Find [imath]f', f'',g', g''[/imath],plug in and simplify.

 

[Loki123]

Simplify things, like no negative exponents.

I Think I solved derivatives correctly. But I can't simplify the expression.

 

[Loki123]

Now just use those y' and y" and evaluate the given expression. It is a dreary calculation but doable.

Do you have the expected answer?

No, I have 4 possible answers

 

[Loki123]

I did it again. I got 0. Is it correct?

 

[BigBeachBanana]

I did it again. I got 0. Is it correct? View attachment 32262

simplify (1+x)^2(n*(sqrt(x^2+1)+x)^n*(n*sqrt(x^2+1)-x))/(x^2+1)^(3/2)+x(n*(sqrt(x^2+1)+x)^n)/sqrt(x^2+1)-n^2(1+sqrt(x^2+1))^n - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

www.wolframalpha.com

 

[Loki123]

simplify (1+x)^2(n*(sqrt(x^2+1)+x)^n*(n*sqrt(x^2+1)-x))/(x^2+1)^(3/2)+x(n*(sqrt(x^2+1)+x)^n)/sqrt(x^2+1)-n^2(1+sqrt(x^2+1))^n - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

www.wolframalpha.com

It's just simplify. I don't see the answer.

 

[Loki123]

Is this correct?

 

[Steven G]

No, the last line is horribly wrong.

Basically you are saying that if 9*0=0, then 9 = 0. NO! 9=9, 9 does not equal 0!

 

[Loki123]

No, the last line is horribly wrong.

Basically you are saying that if 9*0=0, then 9 = 0. NO! 9=9, 9 does not equal 0!

Oh I forgot *0 in the last line

 

[Steven G]

Oh I forgot *0 in the last line

OK!

 

[Loki123]

OK!

so it is 0?

 

[Steven G]

I'm sorry but there is too must work to look through. Please try using a website that will just give you the answer. I hope that you understand. I might miss something that you did wrong. Also getting 0 probably means that you are correct.