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Partial differential of advanced mathematics
w=sinm*e^n

w/? x = cosm(? m/? u)(? u/? x)e^n + sinm*e^n(? n/? v)(? v? x)

= cosm(a^ulna)e^n+sinm*e^n(-sinv)y =(lna)cosm*e^n*a^u-ysinm*e^n*sinv

w/? y = cosm(? m/? u)(? u/? y)e^n + sinm*e^n(? n/? v)(? v? y)

= cosm(a^ulna)e^n+sinm*e^n(-sinv)x =(lna)cosm*e^n*a^u-xsinm*e^n*sinv

^2w/? y? x = lna[-sinm(? m/? u)(? u/? x)e^n*a^u+cosm*a^u*e^n(? n/? v)(? v? x)

+cosm*e^n*a^u*lna(? u/? x)] - sinm*e^n*sinv-x[cosm(? m/? u)(? u/? x)e^n*sinv

+sinm*sinv*e^n(? n/? v)(? v? x)+sinm*e^n*cosv(? v? x)]

=lna[-sinm*(a^ulna)e^n*a^u+cosm*a^u*e^n(-sinv)y+cosm*e^n*a^u*lna]

-sinm*e^n*sinv-x[cosm(a^ulna)e^n*sinv+sinm*sinv*e^n(-sinv)y+sinm*e^n*cosv*y]

=-(lna)^2*sinm*a^(2u)e^n-(lna)(x+y)cosm*a^u*e^n*sinv+(lna)^2cosm*e^n*a*u

sinm*e^n*sinv+xysinm*e^n(sinv)^2-xysinm*e*n*cosv.

^2w/? y^2 = lna[-sinm(? m/? u)(? u/? y)e^n*a^u+cosm*a^u*e^n(? n/? v)(? v? y)

+cosm*e^n*a^u*lna(? u/? y)] - sinm*e^n*sinv-x[cosm(? m/? u)(? u/? y)e^n*sinv

+sinm*sinv*e^n(? n/? v)(? v? y)+sinm*e^n*cosv(? v? y)]

=lna[-sinm*(a^ulna)e^n*a^u+cosm*a^u*e^n(-sinv)x+cosm*e^n*a^u*lna]

-sinm*e^n*sinv-x[cosm(a^ulna)e^n*sinv+sinm*sinv*e^n(-sinv)x+sinm*e^n*cosv*x]

=-(lna)^2*sinm*a^(2u)e^n-2(lna)xcosm*a^u*e^n*sinv+(lna)^2cosm*e^n*a*u

sinm*e^n*sinv+x^2*sinm*e^n(sinv)^2-x^2*sinm*e*n*cosv.