Question

use chain rule to find dw/dt: w = ln (sqr(x^2+y^2+z^2)); x= sint, y = cost, z = tant.
Anyone help me, please

Answer 1

is there supposed to be a z in this problem

Answer 2

yes

Answer 3

let the sqrt (x^2+y^2+z^2) be u for now.
w = ln(u)
dw/dt = 1/u * du/dt

to find du/dt
then let u = sqrt(w) where w = x^2 + y^2 +z^2

so du/dt = 1/2 * w^(-1/2) * dw/dt

then you need dw/dt so use the chain rule to take the derivative of each of the x,y, and z parts with respect to z.


does that help

Answer 4

the formula is \[\frac{ \delta w }{ \delta t } = \frac{ \delta w }{ \delta x }*\frac{ \delta x }{ \delta t } +\frac{ \delta w }{ \delta y } *\frac{ \delta y }{ \delta t } *\frac{ \delta w }{ \delta z } *\frac{ \delta z }{ \delta t }\]

Answer 5

I break it down to find part to part, first, take derivative first part, but i confuse , please , check my answer\[\frac{ \delta w }{ \delta x }\frac{ \delta x }{ \delta t }= \frac{ 1 }{ \sqrt{x^2 +y^2 +z^2} }\frac{ 1 }{ 2\sqrt{x^2+y^2+z^2} }*2xcos t=\frac{ xcos t }{ (x^2+y^2+z^2) }\]

Answer 6

is it right?

Answer 7

yeh, thats right. I usually just tend to do the steps together rather than separate. But yes, you are on the right track.

Answer 8

thanks a lot

Answer 9

just do they exact same thing for the y and z parts and add your answers. You should end up with a common denominator for all three parts.

Answer 10

thanks