## Lymeng_Chhorn 2 years ago Given xz + ylnx + x^2 + 4 define x as differentiable function of two independent variable y and z. Find the value of dx/dz at point (x, y, z) = (1, -1, 3)

1. experimentX

There are three independent variables given that f(x,y,z) = xz + ylnx + x^2 + 4 how do you intent to define x and function of independent variable 'x' and 'y'

2. Lymeng_Chhorn

i got headache with this too ><

3. experimentX

apparently you can put f(x,y,z) = some constant ... sill separating x from those values is quite difficult

4. Lymeng_Chhorn

ooop i forgot xz + ylnx + x^2+ 4 = 0

5. experimentX

still separating x out of ln(x) is quite a challenge. while you can do the last part

6. Lymeng_Chhorn

how can i separate x from lnx do you have any concept to do that?

7. experimentX

the last part requires that ... for separation of x, PDE is the best guess,

8. experimentX

apply product rule

9. Lymeng_Chhorn

xz + ylnx + x^2 + 4 = 0

10. Lymeng_Chhorn

about find the value in the last part i know how to solve it, but about define x as differentiable function of two independent variable y and z i still not clear

11. Lymeng_Chhorn

Thank you all for help

12. experimentX

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