How do you find the derivative of #f(x)=x^8/sin(5x)#? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Massimiliano Mar 1, 2015 The answer is: #y'=(8x^7sin5x-x^8cos5x*5)/(sin^2 5x)=(x^7(8sin5x-5xcos5x))/(sin^2 5x)#. This is for the rules: #y=f(x)/g(x)rArry'=(f'(x)g(x)-f(x)g'(x))/[g(x)]^2# and: #y=sinf(x)rArry'=cosf(x)*f'(x).# 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 2112 views around the world You can reuse this answer Creative Commons License