How do you differentiate #f(x)= e^x/(e^(3-x) -8 )# using the quotient rule?

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Answer 1 · 2016-11-03T16:14:06

#f'(x)=(2e^xe^(3-x)-8e^x)/(e^(3-x)-8)^2#

#f(x)=e^x/(e^(3-x)-8)#

#f= e^x, g=e^(3-x)-8#

#f'=e^x, g'=-e^(3-x)#

#f'(x)=(gf'-fg')/g^2#

#f'(x)=(e^x(e^(3-x)-8)+e^xe^(3-x))/(e^(3-x)-8)^2#

#f'(x)=(e^xe^(3-x)-8e^x+e^xe^(3-x))/(e^(3-x)-8)^2#

#f'(x)=(2e^xe^(3-x)-8e^x)/(e^(3-x)-8)^2#