Find all the first and second order partial derivatives of f(x,y)=−3sin(2x+y)+3cos(x−y).?

A.
Əf/Əx = Ə[-3sin(2x+y) + 3cos(x−y)]/Əx
= -3*[Əsin(2x + y)/Ə(2x+y)]*[Ə(2x+y)/Əx] + 3*[Əcos(x-y)/Ə(x-y)]*[Ə(x-y)/ Əx]
= -3*[cos(2x+y)]*2 + 3*[-sin(x-y)]*1
= -6cos(2x+y) - 3sin(x-y)

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B.
Əf/Əy = Ə[-3sin(2x+y) + 3cos(x−y)]/Əy
= -3*[Əsin(2x + y)/Ə(2x+y)]*[Ə(2x+y)/Əy] + 3*[Əcos(x-y)/Ə(x-y)]*[Ə(x-y)/ Əy]
= -3*[cos(2x+y)]*1 + 3*[-sin(x-y)]*(-1)
= -3cos(2x+y) + 3sin(x-y)

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C.
Əf²/Əx² = Ə(Əf/Əx)/Əx
= Ə[-6cos(2x+y) - 3 sin(x-y)]/Əx
= -6*[Əcos(2x+y)/ Ə(x+y)]*[Ə(2x+y)/Əx] - 3*[Əsin(x-y)/Ə(x-y)]*[ Ə(x-y)/Əx]
= -6*(-sin(2x+y)*2 - 3*cos(x-y)*1
= 12sin(2x+y) - 3cos(x-y)

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D.
Əf²/Əy² = Ə(Əf/Əy)/Əy
= Ə[-3cos(2x+y) + 3sin(x-y)]/Əy
= -3*[Əcos(2x+y)/Ə(2x+y)]*[Ə(2x+y)/Əy] + 3*[Əsin(x-y)/Ə(x-y)]*[Ə(x-y)/Əy]
= -3*(-sin(2x+y)*1 + 3*cos(x-y)*(-1)
= 3sin(2x+y) - 3cos(x-y)

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E.
Əf²/ƏxƏy = Ə(Əf/Əy)/Əx
= Ə[-3cos(2x+y) + 3sin(x-y)]/Əx
= -3*[Əcos(2x+y)/Ə(2x+y)]*[Ə(2x+y)/Əx] + 3*[Əsin(x-y)/Ə(x-y)]*[Ə(x-y)/Əx]
= -3*(-sin(2x+y)*2 + 3*cos(x-y)*(1)
= 6sin(2x+y) + 3cos(x-y)

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F.
Əf²/ƏyƏx = Ə(Əf/Əx)/Əy
= Ə[-6cos(2x+y) - 3 sin(x-y)]/Əy
= -6*[Əcos(2x+y)/ Ə(x+y)]*[Ə(2x+y)/Əy] - 3*[Əsin(x-y)/Ə(x-y)]*[ Ə(x-y)/Əy]
= -6*(-sin(2x+y)*1 - 3*cos(x-y)*(-1)
= 6sin(2x+y) + 3cos(x-y)

OR:
Əf²/ƏyƏx = Əf²/ƏxƏy
= 6sin(2x+y) + 3cos(x-y)

You have been asking this for the past few days. What's the procedure we have been showing you?