00:01
Hello, we have a given function as that is z is equal to f of x comma y that is equal to f of or we can say x square, then we have x square plus of 6 x y minus of y square.
00:22
Now the first part we have the definition of the differential equation difference differential gives as b j z is equal to b z divided by d x with d x plus of b z divided by d y d y.
00:44
Now d z by d x is the here d z by d x is the partial differentiation of z with respect to x and here c y d z divided by d is a partial differentiation of z with respect to y.
01:00
Now from here we can see that is b z divided by d x can be written as that is 2 x plus 6 y and b z divided by d y is equal to 6 x minus of 2 y.
01:18
Now from here putting those value we get the final answer as for first part that is d z is equal to 2 x plus 6 y multiplied by d x plus of 6 x minus of 2 y which is multiplied by d y.
01:36
Now for the second part we have a given that putting x equal to 2 and d x is equal to del x which is equal to 0 .04 and d y that is equal to del y that is equal to 0 .05 and the for value of y that is equal to 3.
02:01
So, putting the value we get the value of b z that is equal to b z is equal to 2 x plus 6 which is multiplied by d x plus of 6 minus of 2 y which is multiplied by d y.
02:16
Now in case of d x we have del x.
02:19
So, putting the value all that value we have 2 multiplied by 2 that is equal to 4 and plus of 6 multiplied by 3 that is equal to 18 which is multiplied by d x so in place of d x we have del x...