L'Hopital's Rule: Solving Homework Statement

[akaliuseheal]

Homework Statement

Can I use L'Hopital's rule here. What I get as a solution is -30/-27 while in the notebook,
without using the L'Hopital's rule the answer is -(2/27)

The attempt at a solution
The derivatives i get are:
x/(x²+5)½
(3x²+2x)/3(x³+x²+15)⅓
2x-5

½ and ⅓ are there because it's easier for me to write it here on this forum like that instead of sqrt.

So..
limx→2( ( x/(x²+5)½ - (3x²+2x)/3(x³+x²+15)⅓ ) / 2x-5 )
Image:

x = 2 ⇒ -30/-27 (1.11)

Could't find software online to verify the solution (symbolab gave no answer) so here I am.
But symbolab did gave me the same answer as I got when I entered the expression from the second image.

 

[Wrichik Basu]

Firstly, please use Latex to write equations. The link to the Latex help is: https://www.physicsforums.com/help/latexhelp/

Now, derivative of $\sqrt{x^2+5}$ is $\dfrac{1}{2} \dfrac{2x}{\sqrt{x^2+5}}$.

The other derivatives are correct.

Put these in. Your answer should come.

 

[member 587159]

Your answer sheet is right. You are wrong.

You calculated the derivative of $(x^3 + x^2 + 15)^{1/3}$ wrong, so that's where your mistake lies.

Also, take a look here:

http://www.wolframalpha.com/input/?...+5}+-+(x^3+++x^2++++15)^(1/3))/(x^2+-+5x+++6)

 

[akaliuseheal]

Firstly, please use Latex to write equations. The link to the Latex help is: https://www.physicsforums.com/help/latexhelp/

Now, derivative of $\sqrt{x^2+5}$ is $\dfrac{1}{2} \dfrac{2x}{\sqrt{x^2+5}}$.

The other derivatives are correct.

Put these in. Your answer should come.

If you look at what you got and then what I got, you will see that those two are the same.

 

[member 587159]

If you look at what you got and then what I got, you will see that those two are the same.

You calculated the other derivative incorrectly. See my post.

 

[akaliuseheal]

Your answer sheet is right. You are wrong.

You calculated the derivative of $(x^3 + x^2 + 15)^{1/3}$ wrong, so that's where your mistake lies.

Also, take a look here:

http://www.wolframalpha.com/input/?i=lim+x->+2+(sqrt{x^2+++5}+-+(x^3+++x^2++++15)^(1/3))/(x^2+-+5x+++6)

Thanks, forgot that to the power of 2 for some reason.