How do you find the derivative of #y=3^sqrtx#? Calculus Differentiating Exponential Functions Differentiating Exponential Functions with Other Bases 1 Answer Shwetank Mauria Jun 22, 2017 #(dy)/(dx)=(3^(sqrtx)ln3)/(2sqrtx)# Explanation: A #y=3^(sqrtx)# #lny=sqrtxln3# and #1/y(dy)/(dx)=1/(2sqrtx)xxln3# or #(dy)/(dx)=ln3/(2sqrtx)xxy=ln3/(2sqrtx)xx3^(sqrtx)=(3^(sqrtx)ln3)/(2sqrtx)# 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 5358 views around the world You can reuse this answer Creative Commons License