How do you differentiate g(y) =(x^3 + x)(4x^2+5) using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Guilherme N. Jan 1, 2016 Product rule states that for y=f(x)g(x), then y'=f'(x)g(x)+f(x)g'(x) Explanation: (dy)/(dx)=(3x^2+1)(4x^2+5)+(x^3+x)(8x) (dy)/(dx)=(12x^4+15x^2+4x^2+5)+(8x^4+8x^2) (dy)/(dx)=20x^4+27x^2+5 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 1734 views around the world You can reuse this answer Creative Commons License