How do you find the derivative of # (e^(2x)) * (cos 2x)#?

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Answer 1 · 2015-12-13T23:08:22

#2e^(2x)(cos(2x)-sin(2x))#

#f'(x)=cos(2x)d/dx[e^(2x)]+e^(2x)d/dx[cos(2x)]#

Find each derivative independently. They both require use of the chain rule.

#d/dx[e^(2x)]=e^(2x)d/dx[2x]=2e^(2x)#

#d/dx[cos(2x)]=-sin(2x)d/dx[2x]=-2sin(2x)#

Plug these back in.

#f'(x)=2e^(2x)cos(2x)-2e^(2x)sin(2x)#

#f'(x)=2e^(2x)(cos(2x)-sin(2x))#