In this case, we use the Chain Rule.
y=3sin5x=3(sinx)5
Let u=sinx so that y=3u5
Taking derivative of u with respect to x , we have:
dxdu=cosx
Similarly, the derivative of y with respect to u is given as
dudy=15u4
By Chain Rule,
dxdy=dudy×dxdu
Therefore, dxdy=15(sinx)4cosx
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