What is the derivative of #sqrt(e^(2x) +e^(-2x))#? Calculus Basic Differentiation Rules Chain Rule 1 Answer Trevor Ryan. Feb 18, 2016 #1/2(e^(2x)+e^(-2x))^(-1/2)*(2e^(2x)-2e^(-2x))# Explanation: We may apply the power rule to obtain : #d/dxsqrt(e^(2x)+e^(-2x))=d/dx(e^(2x)+e^(-2x))^(1/2)# #=1/2(e^(2x)+e^(-2x))^(-1/2)*(2e^(2x)-2e^(-2x))# 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 3096 views around the world You can reuse this answer Creative Commons License