How do i differentiate #xe^(xy)cos(2x)# with respect to x??

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Answer 1 · 2015-02-05T20:10:12

This is actually a multiplication rule within a multiplication rule.

I'm going to evaluate it as:

#(xe^xy)(cos(2x))#

Remember the rule for multiplication:

first(derivative of the 2nd) + second(derivative of the first)

You also need to remember that you must take the derivative of the "inside" of the cos.

#(xe^xy)(-2sin(2x))+(cos(2x))(x(e^(xy)y)+e^(xy))#

#-2xe^(xy)sin(2x)+xye^(xy)cos(2x)+e^(xy)cos(2x)#

We can factor out #e^(xy)#

#e^(xy)(-2xsin(2x)+xycos(2x)+cos(2x))#