How do you differentiate #f(x)=(1+x)(2-x)# using the product rule?

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Answer 1 · 2015-12-01T03:41:33

#f'(x)=1-2x#

According to the product rule, #d/dx[f(x)g(x)]=f'(x)g(x)+f(x)g'(x)#.

We can say that:

#f'(x)=(2-x)d/dx[1+x]+(1+x)d/dx[2-x]#

Note that:

#d/dx[1+x]=1#

#d/dx[2-x]=-1#

Thus:

#f'(x)=(2-x)(1)+(1+x)(-1)#

#f'(x)=2-x-1-x#

#f'(x)=1-2x#