How do you use the Product Rule to find the derivative of #f(x)=e^(4-x)/6#?

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Answer 1 · 2015-08-03T08:28:48

#f'(x)=-(e^(4-x))/6#

To use the product rule we need two functions of #x#, let's take:

#f(x)=(e^(4-x))/6#

=>

#f(x)=g(x)h(x)#

With:

#g(x)=e^4/6# and #h(x)=e^-x#

The product rule states:

#f'=g'h+h'g#

We have:
#g'=0# and #h'=-e^-x#

Therefore:

#f'=(0)(e^-x)+(e^4/6)(-e^-x)=-(e^(4-x))/6#