00:01
Hello everyone, in this problem we are given with the function r of x ,y is given as 3x power 6 minus 2x power 5 y power 6 plus 3x power 7 multiplied by y power 4.
00:18
So, now we need to find all the second order partial derivatives for the given function.
00:24
So, here first we need to find the value of rxx.
00:29
So, now this can be obtained as rxx as the dou square by dou x square of r of x ,y.
00:40
So, now this can be written as substituting the value of the given function here dou square by dou x square of the given function as 3x power 6 minus 2x power 5 y power 6 plus 3x power 7 y power 4.
01:00
So, now differentiating this with respect to x partially.
01:04
So, we have here it would become dou by dou x of 18x power 5 minus 10x power 4 y power 6 plus 21x power 6 y power 4.
01:21
So, now again differentiating this with respect to x we have the required value of rxx as 18 multiplied by 5 is of 90x power 4 minus 10 multiplied by 4 is 40x cube y power 6 plus 21 multiplied by 6 is 126x power 5 y power 4.
01:54
Now, let us find the value of ryy.
02:00
So, ryi is nothing but the partial derivative of the given function with respect to y 2 times that is dou square by dou y square of the function r of x ,y.
02:16
So, now differentiating the given function with respect to y so it would become dou by dou y of so the function would be minus 12x power 5.
02:31
So, here differentiating with respect to y and keeping the x term constant.
02:37
So, it is of minus 12x power 5 y power 5 plus 12x power 7 y cube.
02:48
So, now again differentiating this with respect to y.
02:51
So, we have the value of required value of ryy...