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

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Answer 1 · 2015-10-27T13:02:10

Use the product rule twice (or the three factor product rule once).

#d/dx(uvw) = d/dx(u(vw))#

# = u'(vw)+u[d/dx(vw)]#

# = u'(vw)+u[v'w+vw']#

# = u'vw+uv'w+uvw'#

Apply either the formula or the process to this question with

#u = x# #" "# #" "# #" "##" "# So #u' = x#
#v = e^(x^2)# #" "# #" "##" "##" "# So #v'=2xe^(x^2)#
#w = sin(x^2)# #" "# #" "# So #w' = 2xcos(x^2)#

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