How do you differentiate #f(x)=(x+4)(cosx+2sinx)# using the product rule?

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Answer 1 · 2016-04-12T05:47:02

#(df)/(dx)=cosx(9+2x)-sinx(2+x)#

To differentiate #f(x)=(x+4)(cosx+2sinx)#, we use product rule, which says that if #f(x)=g(x)*h(x)#, then

#(df)/(dx)#=#(dg)/(dx)##h(x)#+#(dh)/(dx)##g(x)# or

As #g(x)=(x+4)# and #h(x)=(cosx+2sinx)# or

#(df)/(dx)=1*(cosx+2sinx)+(-sinx+2cosx)*(x+4)# or

#(df)/(dx)=cosx+2sinx-xsinx+2xcosx-4sinx+8cosx# or

#(df)/(dx)=9cosx-2sinx-xsinx+2xcosx# or

#(df)/(dx)=cosx(9+2x)-sinx(2+x)#