3.I.3A

Vector Calculus | Part IA, 2002

Determine whether each of the following is the exact differential of a function, and if so, find such a function: (a) (cosh⁡θ+sinh⁡θcos⁡ϕ)dθ+(cosh⁡θsin⁡ϕ+cos⁡ϕ)dϕ(\cosh \theta+\sinh \theta \cos \phi) d \theta+(\cosh \theta \sin \phi+\cos \phi) d \phi, (b) 3x2(y2+1)dx+2(yx3−z2)dy−4yzdz3 x^{2}\left(y^{2}+1\right) d x+2\left(y x^{3}-z^{2}\right) d y-4 y z d z.

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