Question

whats the derivative of x on the following function:
xyz(1-x)(2-y)(3-z)

Answer 1

Do you mean what is the partial derivative to that with respect to x?

Answer 2

yes!!

Answer 3

Let me give you a hint
Recall the constant multiple rule
/[yz(2-y)(3-z) \cdot (x(1-x))_x /]

Answer 4

Then use product rule

Answer 5

\[yz(2-y)(3-z) \cdot (x(1-x))_x \]

Answer 6

So what I'm really saying all you need to do is find the derivative of x(1-x) and put that in the parenthesis and bring down the other stuff in front of ( )

Answer 7

so i get: x-x^(2) , and then the partial derivative with respect to x is: x-2x right?

Answer 8

Derivative of x is 1 not x

Answer 9

oh you right, then: 1 - x^(2)

Answer 10

So you almost have it m
yz(2-y)(3-z)(1-2x)
No derivative of x squared is 2x

Answer 11

so: 1 - 2x right?

Answer 12

That is what I have above times the other stuff

Answer 13

You might want to review some basic differentiation rules

Answer 14

so then i have:\[6xy -12x ^{2}y-2xyz+4x ^{2}yz ^{2}-3y ^{2}x+6x ^{2}y-zy ^{2}x+2x ^{2}yz\]

Answer 15

is that the right answer?

Answer 16

I'm not getting that when we multiply the answer out