Find the Derivative – d/da (a^x)^y(a^y)^x

(ax)y(ay)x
Apply the power rule and multiply exponents, (am)n=amn.
dda[axy(ay)x]
Apply the power rule and multiply exponents, (am)n=amn.
dda[axyayx]
Multiply axy by ayx by adding the exponents.
Use the power rule aman=am+n to combine exponents.
dda[axy+yx]
Reorder y and x.
dda[axy+xy]
dda[a2xy]
dda[a2xy]
dda[a2xy]
Differentiate using the Power Rule which states that dda[an] is nan-1 where n=2xy.
2xya2xy-1
Reorder the factors of 2xya2xy-1.
2a2xy-1xy
Find the Derivative – d/da (a^x)^y(a^y)^x

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