What is the derivative of x^(3/x)x3x? Calculus Differentiating Exponential Functions Differentiating Exponential Functions with Other Bases 1 Answer Luke Phillips Jun 4, 2017 "d"/("d"x) x^(3/x) = (ln(3/x)-3)*x^(3/x)ddxx3x=(ln(3x)−3)⋅x3x Explanation: Write x^(3/x) = exp(-xln(x/3))x3x=exp(−xln(x3)). Then, by the chain rule, "d"/("d"x) x^(3/x) = exp(-xln(x/3))*"d"/("d"x)(-xln(x/3))ddxx3x=exp(−xln(x3))⋅ddx(−xln(x3)), "d"/("d"x) x^(3/x) = exp(-xln(x/3))*(-ln(x/3)-x*1/(x/3))ddxx3x=exp(−xln(x3))⋅(−ln(x3)−x⋅1x3), "d"/("d"x) x^(3/x) = exp(-xln(x/3))*(ln(3/x)-3)ddxx3x=exp(−xln(x3))⋅(ln(3x)−3), "d"/("d"x) x^(3/x) = (ln(3/x)-3)*x^(3/x)ddxx3x=(ln(3x)−3)⋅x3x. 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 1622 views around the world You can reuse this answer Creative Commons License