Question #9ef93 Calculus Basic Differentiation Rules Product Rule 1 Answer 冠廷 李. Jun 17, 2016 f'(x)=4(2x-6)^3*2(x^2+1)^5+(2x-6)^4*5(x^2+1)^4*2x Explanation: assume exist f(x)=(2x-6)^4(x^2+1)^5 use chain rule d/dx(2x-6)^4=4(2x-6)^3d/dx(2x-6)=4(2x-6)^3*2 same concept d/dx(x^2+1)^5=5(x^2+1)^4*2x f'(x)=4(2x-6)^3*2(x^2+1)^5+(2x-6)^4*5(x^2+1)^4*2x 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 1499 views around the world You can reuse this answer Creative Commons License