How do you differentiate #y=x^(x-1)#? Calculus Differentiating Exponential Functions Differentiating Exponential Functions with Other Bases 1 Answer Alan N. Dec 21, 2016 #dy/dx= x^(x-1)*((x-1)/x+lnx)# Explanation: #y=x^(x-1)# #lny = (x-1)*lnx# #1/ydy/dx= (x-1)*1/x+lnx*1# #dy/dx= y * ((x-1)*1/x+lnx)# #dy/dx= x^(x-1)*((x-1)/x+lnx)# 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 1896 views around the world You can reuse this answer Creative Commons License