00:01
In this problem we are provided with the equation 2 times x squared plus y squared equals to 6 and we are asked to find out y double prime by making use of implicit differentiation.
00:15
So let us mark the given question as equation 1.
00:19
Now let us differentiate it.
00:20
So we have 2 times the derivative of x squared is 2 times x plus the derivative of y squared is 2 times y times y times y prime by chain rule.
00:31
And the derivative of any constant is 0.
00:34
So here, dividing by 2 throughout, we get 2 times x plus y times y prime equals to 0.
00:42
So now we need to solve for y prime.
00:46
So we have y times y prime to be equal to negative 2x and dividing by y on both sides we have y prime to be equal to negative 2x over y.
00:57
So next let us again differentiate the obtained equation.
01:01
Since we need to obtain y double prime.
01:04
So differentiating it one more time, we have two times the derivative of x is one plus over here we have the product of two functions.
01:14
So we make use of the product rule.
01:16
So first we differentiate y.
01:18
We get y prime and y prime remains as it is plus now y remains as it is differentiating y prime.
01:25
We get y double prime and this equals to zero...