How do you find the derivative of # 5^(x^2)#? Calculus Differentiating Exponential Functions Differentiating Exponential Functions with Other Bases 1 Answer bp Aug 2, 2015 #5^(x^2) 2x ln5# Explanation: Let y = # 5^(x^2)# ln y= #x^2 ln5#. Now differentiate w.rt. x both sides, #1/y dy/dx = 2x ln5# #dy/dx = 5^(x^2) 2x ln 5# 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 1600 views around the world You can reuse this answer Creative Commons License