Question #b5198 Calculus Differentiating Logarithmic Functions Overview of Different Functions 1 Answer Joel Kindiak Jun 6, 2016 #dy/dx = (x-1)/(2x ln 5)# Explanation: First, simplify the given expression. #y=log_25 (e^x)-log_5 (x^(1/2))=ln (e^x)/(2ln5)-1/2 (ln x / ln 5) = 1/(2 ln5)(x-ln x)# #dy/dx = 1/(2ln5) (1-1/x) = (x-1)/(2x ln 5)# Answer link Related questions How do you find the derivative of #y=sin2x+cos2x+ln(ex)#? What is the derivative of #y= e^(3x/4)#? What is the derivative of #y= 2x^4 - 2x^3 - 8#? What is the derivative of #y=ln[x/(2x+3)]^(1/2)#? What is the derivative of # e^(x^3)+log_5(pi)#? What is the derivative of #ln(x^2)#? What is the derivative of #1/logx#? Question #09fd4 Question #56c3f See all questions in Overview of Different Functions Impact of this question 2276 views around the world You can reuse this answer Creative Commons License