dana.king

Help,

My teacher assigned an extra assignment for our class, to help boost
our grades for University application. Unfortunately, I have been
unable to solve one of the problems. My teacher gave us the fully
simplified answer, but I have been unable to get the same answer.

The question reads: Given: 4x^2 - 5y^2 = -1 . Simplify Fully.

The answer is: 4/25 y^3 <----How do i get this?

Any help with this solution would be greatly, appreciated.

Thank you

ken pledger

First, I think you meant the question to include "Find the second
derivative y'' of y with respect to x." Second, the answer is
actually 4/(25 y^3) i.e. with the y^3 in the denominator.

You need to think of the equation 4x^2 - 5y^2 = -1 as defining a
function intrinsically, and differentiate the whole equation:

8x - 10 y y' = 0.

The term 10 y y' comes from the chain rule: (d(5 y^2)/dy)(dy/dx).

Now you can find y' in terms of x and y, differentiate again to
find y'', and simplify. This problem is artificially rigged so that
the answer includes (4 x^2 - 5 y^2) which you can simplify from the
original equation.

Can you make progress now?

Ken Pledger.