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 1690 views around the world You can reuse this answer Creative Commons License