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How do you differentiate #f(x)=e^(x^2)/(e^(2x)-2x)# using the quotient rule?

1 Answer

Nov 30, 2015

#f'(x)=(2e^(x^2)(xe^(2x)-2x^2-e^(2x)+1))/(e^(2x)-2x)^2#

Explanation:

According to the quotient rule:

#f'(x)=((e^(2x)-2x)overbrace(d/dx[e^(x^2)])^(2xe^(x^2))-e^(x^2)overbrace(d/dx[e^(2x)-2x])^(2e^(2x)-2))/(e^(2x)-2x)^2#

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

#f'(x)=(2e^(x^2)(xe^(2x)-2x^2-e^(2x)+1))/(e^(2x)-2x)^2#

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