Find y'' by implicit differentiation

[bobraymund]

Homework Statement

Find y'' by implicit differentiation.

Homework Equations

The Attempt at a Solution

I get to this point in the problem, which is I solved for y'. But then when I attempt to take y'', in other words take the derivative of my answer for y', I don't get the answer that is in the back of the book.

Many thanks in advance,
Bob

 

[Mark44]

You went astray in the 2nd line and all following lines. The second line should be
18x + 2y dy/dx = 0 and your last line should be dy/dx = -9x/y. Now take the derivative again, keeping in mind that you need to use the quotient rule and the chain rule, in that order.

 

[rock.freak667]

so y*y'=-9x

so take d/dx of both sides

for d/dx(y*y') use the product rule .

 

[blake knight]

Bob, your last equation can be rewritten as; y'=-9xy^-1---->from here here you may get the y" by product rule and arrive at having y"=9/y^2(x-y)--->is this what you got in your book?

 

[blake knight]

You can rewrite your last equation to: yy'=-9x---> from here try implicit differentiation.
You'll arrive at having: yy"+y'y'=-9; next, substitute the value of y'=-9x/y (previously derived); You'll arrive at having: y"=-9/y^3(9x^2+y^2).