How do you differentiate #y=(3/2)^x#? Calculus Differentiating Exponential Functions Differentiating Exponential Functions with Other Bases 1 Answer Tazwar Sikder Sep 15, 2016 #((3) / (2))^(x) cdot ln((3) / (2))# Explanation: We have: #y = ((3) / (2))^(x)# The derivative of any function of the form #f(x) = a^(x)# is given as: #f'(x) = a^(x) ln(a)# #=> (d) / (dx) (((3) / (2))^(x)) = ((3) / (2))^(x) cdot ln((3) / (2))# Answer link Related questions How do I find #f'(x)# for #f(x)=5^x# ? How do I find #f'(x)# for #f(x)=3^-x# ? How do I find #f'(x)# for #f(x)=x^2*10^(2x)# ? How do I find #f'(x)# for #f(x)=4^sqrt(x)# ? What is the derivative of #f(x)=b^x# ? What is the derivative of 10^x? How do you find the derivative of #x^(2x)#? How do you find the derivative of #f(x)=pi^cosx#? How do you find the derivative of #y=(sinx)^(x^3)#? How do you find the derivative of #y=ln(1+e^(2x))#? See all questions in Differentiating Exponential Functions with Other Bases Impact of this question 1565 views around the world You can reuse this answer Creative Commons License