Can someone please explain the solution for Q23. I know how to do it using the long way (calculating all derivatives and summing them up) but can someone please explain the shortcut mentioned in the answers?
Not sure about the shortcut mentioned as I can't find it in the answers, but for the first term you can see that each derivative is just 3 for all six variables so add 3*6 = 18
for the next we have three variables to the same power(2) so add 2 x 3 = 18
For the -7xz^5 term we can see that it will evaluate into (-7 - 35) so subtract -42
We have \(x=y=z=u=v=w=1\) but essentially what matters in the first place is that \(x=y=z=u=v=w\), so the function becomes \(f(x,x,x,x,x,x)=3x^6+x^6-7x^6+3x^6=0\), which derivative gives 0 too, and hence the result
Q23
Can someone please explain the solution for Q23. I know how to do it using the long way (calculating all derivatives and summing them up) but can someone please explain the shortcut mentioned in the answers?
Thanks a lot!
Not sure about the shortcut mentioned as I can't find it in the answers, but for the first term you can see that each derivative is just 3 for all six variables so add 3*6 = 18
for the next we have three variables to the same power(2) so add 2 x 3 = 18
For the -7xz^5 term we can see that it will evaluate into (-7 - 35) so subtract -42
similarly for the last term 3 x 4 + 3 x 2 = 18
18 + 18 + 6 - 42 = 0
1
We have \(x=y=z=u=v=w=1\) but essentially what matters in the first place is that \(x=y=z=u=v=w\), so the function becomes \(f(x,x,x,x,x,x)=3x^6+x^6-7x^6+3x^6=0\), which derivative gives 0 too, and hence the result
2
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