How do you differentiate #f(x)= e^x(4x-4)# using the product rule?

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Answer 1 · 2017-06-28T13:31:27

#(df)/(dx)=4xe^x#

Product rule states if #f(x)=g(x)h(x)#

then #(df)/(dx)=(dg)/(dx)xxh(x)+(dh)/(dx)xxg(x)#

Here we have #f(x)=g(x)h(x)#, where #g(x)=e^x# and #h(x)=4x-4#

Therefore #(dg)/(dx)=e^x# and #(dh)/(dx)=4#

Hence #(df)/(dx)=e^x(4x-4)+4e^x#

= #e^x(4x-4+4)#

= #4xe^x#