How do you differentiate f(x)=x^6/e^(x-6) using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Sasha P. Oct 30, 2015 f'(x)=(x^5(6-x))/e^(x-6) Explanation: f'(x)=(u'v-uv')/v^2 u=x^6 => u'=6x^5 v=e^(x-6) => v'=e^(x-6)*(x-6)'=e^(x-6)*1=e^(x-6) f'(x)=(6x^5e^(x-6)-x^6e^(x-6))/(e^(x-6))^2 = (x^5e^(x-6)(6-x))/(e^(x-6))^2 f'(x)=(x^5(6-x))/e^(x-6) 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 1806 views around the world You can reuse this answer Creative Commons License