Question

Find the differential of the function w=x^3sin(y^6z^3)

This is what I got but its not correct.
dw=3x^3y^6z^2cos(y^6z^3)
dx=3x^2sin(y^6z^3)
dy=6x^3y^5z^3cos(y^6z^3)

Where am I going wrong?

Answer 1

First of all, this is a function that includes more than one variable, so when you are going to differentiate it, seclect one variable to take the derivative with respect to it.

Answer 2

That is what I did, or was attempting to do anyway. In the case of x, I only took the derivative of x, treating the rest as constants

Answer 3

Good concept, but you wrote dw, although there is not w-variable in that equation!!

Answer 4

dw is actually one of the questions I am supposed to answer, which has me confused.

Answer 5

They said
\[dw= \dfrac{\partial w}{\partial x}+\dfrac{\partial w}{\partial y}+\dfrac{\partial w}{\partial z}\]

Answer 6

\(\dfrac{\partial w}{\partial x}= 3x^2sin(y^6z^3)\)

Answer 7

do the same with y and z.

Answer 8

Loser66 is right.

Answer 9

Ah ok, thanks. that makes sense with respect to dw. However, the answer for x that you posted is the same I got but I was told it is incorrect

Answer 10

Not the same!!

Answer 11

Your answer: \(3x^3y^6z^2cos (y^6z^3)\)

My answer: \(3x^2sin(y^6z^3)\)

Answer 12

shouldn't it be

\(dw= \dfrac{\partial w}{\partial x} \color{red}{dx}+\dfrac{\partial w}{\partial y} \color{red}{dy}+\dfrac{\partial w}{\partial z} \color{red}{dz}\)

...which is called the **total differential**

Answer 13

That was the answer I had for dw, but if you look at the attacked screen shot, my dx is \[3x ^{2}\sin(y ^{6}z ^{3}\]

Answer 14

hey @IrishBoy123 how do you change font colour?