Can somebody explain how to find the derivative of f(x)=xyz?

Question

I think someone said that it's 0 but i'm not sure how to get to that. The x, y, and z are constants I believe. Anyways, please solve step by step if anyone knows. Thanks

Answer 1

This derivative will not be zero.

f(x)=xyz implies that x is a variable, and y and z are constants. So treat it like 2x--the derivative of which is just the constant value. So it'll be yz in this case.

In multivariable calculus, there is something like a partial derivative. This acts pretty much the same way, in that you treat all variables, but the one you're deriving, as constants.

Answer 2

Alright here's the answer to cover a few possibilities.

If you are talking about partial derivatives and in this case you are differentiating with respect to x then you consider yz as constants and differentiate x which leaves f(x) = yz.

If you are stating that they are ALL constants then the answer is simple and the derivative of xyz = 0.

Answer 3

If all three are constants, then the derviative is zero.

I doubt that is the whole problem. Get some more information and ask again.

Answer 4

x cannot be constant as we are finding derivative wrt x(say)

y and z may or may nor be

Let us assume they are not. In case they are dy/dx = 0 or dz/dx = 0 as the case may be

use the product rule
using d/dx(uv) = u dv/dx + v du/dx u =x and v = yz

f = xyz
df/dx = x.d/dx(yz) + yz (dx/dx)
= x d/dx(yz) + yz
= xy dz/dx + xz dy/dx + yz(again product rule)

Answer 5

If the function is f(x), then x is NOT a constant. Are you sure you read that right?

Answer 6

f(x)=xyz
f'(x)=(differentiate x)(keep yz as it is)+(differentiate y)(keep xz as it is)+)+(Differentiate x)(keep yzas it is)+(differentiate z)(keep xyas it is)

f'(x)= yz+(dy/dx) xz +(dz/dx)( xy)

Answer 7

f(x)=(x)x(y)x(Z)
(y)x(z)=f