What is the derivative of #x^sin(x)#? Calculus Differentiating Exponential Functions Differentiating Exponential Functions with Other Bases 1 Answer Sonnhard Jul 11, 2018 #f'(x)=e^(sin(x))*cos(x)# Explanation: After the chain rule #(f(g(x))'=f'(g(x))*g'(x)# we get #f'(x)=e^(sin(x))*cos(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 1629 views around the world You can reuse this answer Creative Commons License