Second Derivative Value via Implicit Differentiation

Hi guys, I haven't posted in a while but I was tutoring someone and ran into a problem that I thought had got right but blackboard said was incorrect.

The problem is

Now find the second derivative when x = 2 and y =1

I keep getting 3/4 as my answer. I solved it using implicit differentiation and also using partials differentiation to double check. The correct answer according to blackboard is -14/27

and can someone show me what im doing wrong with my latex. Guess im a bit rusty. Thanks

Aug 3rd 2011, 10:26 PM

pickslides

re: Second Derivative Value via Implicit Differentiation

Quote:

Originally Posted by 11rdc11

and can someone show me what im doing wrong with my latex. Guess im a bit rusty. Thanks

Use "tex" tags, "math" tags are no good here at the moment

Aug 3rd 2011, 10:27 PM

FernandoRevilla

re: Second Derivative Value via Implicit Differentiation

Quote:

Originally Posted by 11rdc11

Hi guys, I haven't posted in a while but I was tutoring someone and ran into a problem that I thought had got right but blackboard said was incorrect.

The problem is

Now find the second derivative when x = 2 and y =1

I keep getting 3/4 as my answer. I solved it using implicit differentiation and also using partials differentiation to double check. The correct answer according to blackboard is -14/27

and can someone show me what im doing wrong with my latex. Guess im a bit rusty. Thanks

Your function is defined by . Deriving: . Substituting we get or equivalently . Derive again and substitute .

Aug 3rd 2011, 10:48 PM

11rdc11

re: Second Derivative Value via Implicit Differentiation

Thanks guys but even when i take the second derivative i get the same

now taking the derivative again

which simplifies to

and plugging in the values you 3/4 right?

Aug 3rd 2011, 10:54 PM

pickslides

re: Second Derivative Value via Implicit Differentiation

Quote:

Originally Posted by 11rdc11

and plugging in the values you 3/4 right?

Looks good to me.

Aug 3rd 2011, 11:01 PM

11rdc11

re: Second Derivative Value via Implicit Differentiation

Thanks that is what I thought but it kept telling me that I was wrong.

Aug 3rd 2011, 11:02 PM

FernandoRevilla

re: Second Derivative Value via Implicit Differentiation

Deriving we get . Substituting you'll obtain .

Aug 4th 2011, 12:00 AM

CaptainBlack

re: Second Derivative Value via Implicit Differentiation

Quote:

Originally Posted by pickslides

Use "tex" tags, "math" tags are no good here at the moment

You mean "Jedi math tags do not work on MHF ony tex..."

CB

Aug 4th 2011, 04:16 AM

tom@ballooncalculus

Re: Second Derivative Value via Implicit Differentiation

Quote:

Originally Posted by 11rdc11

now taking the derivative again

A point against the quotient rule? Many people prefer to see the quotient as a product, anyway. Just in case a picture helps...

... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case x), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

But this is wrapped inside the legs-uncrossed version of...