How do you differentiate #f(x)=(x^2)/(e^(x^-3))# using the quotient rule?

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How do you differentiate #f(x)=(x^2)/(e^(x^-3))# using the quotient rule?

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Answer 1 · 2016-10-19T19:07:58

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

Explanation:

The quotient rule is #d/dx(u/v)=(v(du)/dx - u(dv)/dx)/v^2#

So, # f(x)=x^2/e^(x-3) #
# :. f'(x) = ( e^(x-3) d/dx(x^2)-x^2d/dx(e^(x-3)) ) / (e^(x-3))^2 #
# :. f'(x) = ( e^(x-3) (2x)-x^2(e^(x-3)) ) / (e^(x-3))^2 #
# :. f'(x) = ( e^(x-3) (2x-x^2) ) / (e^(x-3))^2 #
# :. f'(x) = ( (2x-x^2) ) / (e^(x-3)) #
# :. f'(x) = ( x(2-x) ) / (e^(x-3)) #

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How do you differentiate #f(x)=(x^2)/(e^(x^-3))# using the quotient rule?

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