Step-by-step explanation:
[tex]w = x^4\sin(y^4z^3)[/tex]
The differential [tex]dw[/tex] is
[tex]dw = 4x^3\sin(y^4z^3)dx [/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:+ x^4\cos(y^4z^3)(4y^3z^3)dy [/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+ x^4\cos(y^4z^3)(3y^4z^2)dz[/tex]
