How do you differentiate #f(x)=xe^(3x)# using the product rule?

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Answer 1 · 2017-01-10T08:40:47

#f'(x)=e^(3x)(1+3x)#

The product rule for differentiation is:

#f(x)=uv,# where #u# & #v# are both functions of #x#

#f'(x)=vu'+uv'#

#f(x)=xe^(3x)#

#u=x=>u'=1#

#v=e^(3x)=>v'=3e^(3x)#

#:.f'(x)=e^(3x)xx1+x xx3e^(3x)#

#f'(x)=e^(3x)+3xe^(3x)#

#f'(x)=e^(3x)(1+3x)#