How do you differentiate f(x) = x^3/sinx using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer moutar Jan 14, 2016 (x^2(3sinx-xcosx))/sin^2x Explanation: The quotient rule states that: d/dx(u/v)=(vu'-uv')/v^2 u=x^3, v=sinx u'=3x^2, v'=cosx d/dx(x^3/sinx)=(sinx*3x^2-x^3*cosx)/sin^2x =(x^2(3sinx-xcosx))/sin^2x 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 2108 views around the world You can reuse this answer Creative Commons License