Is This Calculation of ∂z/∂x Correct for the Given Function?

[njo]

Homework Statement

∂z/∂x of ycos(xz)+(4xy)-2z^2x^3=5x[/B]

Homework Equations

n/a

The Attempt at a Solution

∂z/∂x=(5+yz-4y+6z^2x^2)/(-yxsin(xz)-4zx^3)[/B]

Is this correct? Just trying to make sure that's the correct answer. I appreciate the help. I can post my work if need be. Thanks

 

[LCKurtz]

Close, but check your work. There is at least a sine term missing in the numerator. Better yet, show your work.

 

[njo]

-y*sin(xz)*(z+x(∂z/∂x))+4y-4zx^3(∂z/∂x)-6z^2x^2 = 5

This is what I have before rearranging and factoring for ∂z/∂x

 

[LCKurtz]

-y*sin(xz)*(z+x(∂z/∂x))+4y-4zx^3(∂z/∂x)-6z^2x^2 = 5

This is what I have before rearranging and factoring for ∂z/∂x

That looks good. If you carefully do the algebra solving for $\frac{\partial z}{\partial x}$ you should be OK.

 

[njo]

(5+yzsin(xz)-4y+6z^2x^2)/(-yxsin(xz)-4zx^3) = ∂z/∂x

Pretty sure this is right. Just messed up on my algebra. Thank you so much. The internet is great.