00:01
Hi, from the question given that consider the given equation x squared plus 2xy minus y squared plus 8 is equal to 0.
00:13
From this we need to find the second derivative that is d squared y by dx squared is the thing we need to find here.
00:22
So, from this 2xy minus y squared plus 8 is equal to minus x squared.
00:31
So, here 2xy minus y squared is equal to minus x squared minus 8.
00:37
So, from this now differentiating implicitly so we obtain 2x times of dx by dx is 1 plus 2 times of here we need to use the product rule x times dy by dx plus y times 1 minus 2y dy by dx plus 0 is equal to 0.
01:05
So, here 2x plus 2x dy by dx plus 2y minus 2y dy by dx is equal to 0.
01:21
Now again differentiating so we obtain 2 times of 1 plus 2 times of x d squared y by dx squared plus dy by dx times of 1 plus 2 times of dy by dx minus 2 here also we need to use the product rule y times of d squared y by dx squared and plus dy by dx times of dy by dx which is equal to 0.
02:08
So, for further simplification 2 plus 2x d squared y by dx squared plus 2 dy by dx plus 2 dy by dx minus 2y d squared y by dx squared minus 2 dy by dx the whole square is equal to 0.
02:38
Now from this equation we need to find the value of dy by dx...