How do you differentiate #f(x)= (4x^2+5)*e^(x^2)# using the product rule?

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Answer 1 · 2016-10-18T02:43:52

#f'(x)=2xe^(x^2)(4x^2+9)#

Product rule: #f'(x)=u'v+v'u#

#f(x)=(4x^2+5)*e^(x^2)#

Let #u=4x^2+5# and #v=e^(x^2)#

#u'=8x#
#v'=2xe^(x^2)#

#:.f'(x)=8x*e^(x^2)+2xe^(x^2)*(4x^2+5)#

#=2xe^(x^2)(4+4x^2+5)#

#=2xe^(x^2)(4x^2+9)#