How do you find the derivative of #Y= ( 2x + 9 ) sqrt(x^2 - 4)#? Calculus Basic Differentiation Rules Product Rule 1 Answer Andy Y. Aug 4, 2015 #Y'=(2x+9)*x/(sqrt(x^2-4))+2*sqrt(x^2-4)# Explanation: Let #f(x)=2x+9# and #g(x)=sqrt(x^2-4)#. Their derivatives are: #f'(x)=2# and #g'(x)=1/2(x^2-4)^(-1/2)*2x=x/(sqrt(x^2-4))# The Product Rule says that #Y'=f(x)g'(x)+f'(x)g(x)# #Y'=(2x+9)*x/(sqrt(x^2-4))+2*sqrt(x^2-4)# 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 1667 views around the world You can reuse this answer Creative Commons License