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 1341 views around the world You can reuse this answer Creative Commons License