How do you differentiate f(x)=e^sqrt(3lnx+x^2) using the chain rule.? Calculus Basic Differentiation Rules Chain Rule 1 Answer moutar Jan 16, 2016 dy/dx=(e^sqrt(3lnx+x^2) * (3/x+2x))/((2sqrt(3lnx+x^2)) Explanation: The chain rule: dy/dx=dy/(du) * (du)/(dv)*(dv)/(dx) y = e^u, dy/(du)=e^u u=v^(1/2), (du)/(dv)=1/2v^-(1/2) v=3lnx+x^2, (dv)/dx=3/x+2x dy/dx=e^u*1/(2sqrtv)*(3/x+2x) dy/dx=(e^sqrt(3lnx+x^2) * (3/x+2x))/((2sqrt(3lnx+x^2)) Answer link Related questions What is the Chain Rule for derivatives? How do you find the derivative of y= 6cos(x^2) ? How do you find the derivative of y=6 cos(x^3+3) ? How do you find the derivative of y=e^(x^2) ? How do you find the derivative of y=ln(sin(x)) ? How do you find the derivative of y=ln(e^x+3) ? How do you find the derivative of y=tan(5x) ? How do you find the derivative of y= (4x-x^2)^10 ? How do you find the derivative of y= (x^2+3x+5)^(1/4) ? How do you find the derivative of y= ((1+x)/(1-x))^3 ? See all questions in Chain Rule Impact of this question 1819 views around the world You can reuse this answer Creative Commons License