How do you differentiate #f(x)=11xe^(2x)# using the product rule?

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Answer 1 · 2018-04-17T13:15:49

#f'(x)=11e^(2x)(2x+1)#

The Product Rule tells us for two functions #f, g# multiplied together, we take the derivative as follows:

#(fg)'=fg'+gf'#

So, for #f(x)=11xe^(2x),#

#f'(x)11xd/dxe^(2x)*e^(2x)d/dx11x#

#d/dx11x=11#

#d/dxe^(2x)=2e^(2x)#
S
Then,

#f'(x)=22xe^(2x)+11e^(2x)#

Simplify:

#f'(x)=11e^(2x)(2x+1)#