How do you differentiate #f(x)=(x^2)/(e^(x^-3))# using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Steve M Oct 19, 2016 # 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)) # Answer link Related questions What is the Quotient Rule for derivatives? How do I use the quotient rule to find the derivative? How do you prove the quotient rule? How do you use the quotient rule to differentiate #y=(2x^4-3x)/(4x-1)#? How do you use the quotient rule to differentiate #y=cos(x)/ln(x)#? How do you use the quotient rule to find the derivative of #y=tan(x)# ? How do you use the quotient rule to find the derivative of #y=x/(x^2+1)# ? How do you use the quotient rule to find the derivative of #y=(e^x+1)/(e^x-1)# ? How do you use the quotient rule to find the derivative of #y=(x-sqrt(x))/(x^(1/3))# ? How do you use the quotient rule to find the derivative of #y=x/(3+e^x)# ? See all questions in Quotient Rule Impact of this question 1205 views around the world You can reuse this answer Creative Commons License