How do you differentiate y=(x^4+3)(-4x^5+5x^4+5) using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer loa Apr 3, 2017 y'=-4x^3(9x^5-10x^4+15x-20) Explanation: Denote f(x)=x^4+3 and g(x)=-4x^5+5x^4+5 so that y is of the form f.g. The derivative of y with respect to x according the product rule is then f'.g+f.g': y' =f'.g+f.g' y'=(4x^3)(-4x^5+5x^4+5)+(x^4+3)(-20x^4+20x^3) y'=-16x^8+20x^7+20x^3-20x^8+20x^7-60x^4+60x^3 y'=-36x^8+40x^7-60x^4+80x^3 y'=-4x^3(9x^5-10x^4+15x-20) Answer link Related questions What is the Product Rule for derivatives? How do you apply the product rule repeatedly to find the derivative of f(x) = (x - 3)(2 - 3x)(5 - x) ? How do you use the product rule to find the derivative of y=x^2*sin(x) ? How do you use the product rule to differentiate y=cos(x)*sin(x) ? How do you apply the product rule repeatedly to find the derivative of f(x) = (x^4 +x)*e^x*tan(x) ? How do you use the product rule to find the derivative of y=(x^3+2x)*e^x ? How do you use the product rule to find the derivative of y=sqrt(x)*cos(x) ? How do you use the product rule to find the derivative of y=(1/x^2-3/x^4)*(x+5x^3) ? How do you use the product rule to find the derivative of y=sqrt(x)*e^x ? How do you use the product rule to find the derivative of y=x*ln(x) ? See all questions in Product Rule Impact of this question 2856 views around the world You can reuse this answer Creative Commons License