How do you find the derivative of #3^(x^2)#? Calculus Differentiating Exponential Functions Differentiating Exponential Functions with Other Bases 1 Answer Andrea S. Jan 3, 2017 #d/(dx) 3^(x^2) =2xln3 *3^(x^2)# Explanation: Note that: #3^(x^2) = (e^ln3)^(x^2)= e^(ln3x^2)# Using the chain rule: #d/(dx) 3^(x^2) = d/(dx) e^(ln3x^2) = e^(ln3x^2)*d/(dx) (ln3x^2) = 2ln3xe^(ln3x^2)=2ln3 x 3^(x^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 1235 views around the world You can reuse this answer Creative Commons License