How would you find the first derivative of f(x) = (5-x)x^(2/3)f(x)=(5−x)x23? Calculus Basic Differentiation Rules Product Rule 1 Answer Gió Mar 31, 2015 I would use the Product Rule: f'(x)=-1*x^(2/3)+(5-x)2/3x^(-1/3)= =-x^(2/3)+10/3x^(-1/3)-2/3x^(2/3)= =-x^(2/3)[1+2/3]+10/3x^(-1/3)= =-x*x^(-1/3)[5/3]+10/3x^(-1/3)= =-5(x-2)/(3root3(x)) 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 1902 views around the world You can reuse this answer Creative Commons License