What is the derivative of #x^(3/x)#? 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)# Explanation: Write #x^(3/x) = exp(-xln(x/3))#. Then, by the chain rule, #"d"/("d"x) x^(3/x) = exp(-xln(x/3))*"d"/("d"x)(-xln(x/3))#, #"d"/("d"x) x^(3/x) = exp(-xln(x/3))*(-ln(x/3)-x*1/(x/3))#, #"d"/("d"x) x^(3/x) = exp(-xln(x/3))*(ln(3/x)-3)#, #"d"/("d"x) x^(3/x) = (ln(3/x)-3)*x^(3/x)#. 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 1323 views around the world You can reuse this answer Creative Commons License