What is the derivative of #x*x^(1/2)#? Calculus Basic Differentiation Rules Product Rule 2 Answers P dilip_k Mar 18, 2016 #=3/2x^(1/2)# Explanation: #d/dx(x*x^(1/2))=d/dx(x^(1/2+1))=d/dx(x^(3/2))=3/2x^(3/2-1)=3/2x^(1/2)# Answer link ali ergin Mar 18, 2016 #d/(d x)(x*x^(1/2))=3/2*sqrt x# Explanation: #d/(d x)(x*x^(1/2))=d/(d x) (x)*x^(1/2)+d/(d x)(x^(1/2))*x# #d/(d x)(x*x^(1/2))=1*x^(1/2)+1/2*(x^(1/2-1))*x# #d/(d x)(x*x^(1/2))=x^(1/2)+1/2*x^(1/2)# #d/(d x)(x*x^(1/2))=x^(1/2)(1+1/2)# #d/(d x)(x*x^(1/2))=3/2*sqrt 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 1797 views around the world You can reuse this answer Creative Commons License