What is the derivative of (3^(2t))/t? Calculus Differentiating Exponential Functions Differentiating Exponential Functions with Other Bases 1 Answer Alan N. Sep 24, 2016 f'(t) = ((2ln3*t-1)*3^(2t))/t^2 Explanation: f(t)=3^(2t)/t = 3^(2t)*t^-1 ln f(t) = 2t*ln3-lnt Using implicit differentiation: 1/f(t)*f'(t) = 2t*0 + 2*ln3 -1/t (Product rule and standard differential) 1/f(t)*f'(t) = 2ln3-1/t Since f(t)=3^(2t)/t f'(t) = 3^(2t)/t * (2ln3-1/t) = = ((2ln3*t-1)*3^(2t))/t^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 3581 views around the world You can reuse this answer Creative Commons License