Find the differential. a) z=\frac{1}{2}(e^{x^{2}+y^{2}}-e^{-x^{2}-y^{2}}) b) w=2z^{3}y\sin x

fertilizeki 2021-12-13 Answered
Find the differential.
a) z=12(ex2+y2ex2y2)
b) w=2z3ysinx
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Expert Answer

limacarp4
Answered 2021-12-14 Author has 39 answers
Step 1
We have to find the differential
a) z=12(ex2+y2ex2y2)
Step 2
dz=12[ex2+y2(2x)ex2y2(2x)]dx+12[ex2+y2(2y)ex2y2(2y)]dy
dz=x(ex2+y2+ex2y2)dx+y(ex2+y2+ex2y2)dy

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Jeremy Merritt
Answered 2021-12-15 Author has 31 answers
Step 3
b) w=2z3ysinx (ddx(xn)=nxn1)
then
dω=6z2ysinxdz+2z3sinxdy+2x3ycosndz
(ddx(sinx)=cosx)

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