How do you find the derivative of # (sin x)^cos x #? Calculus Basic Differentiation Rules Summary of Differentiation Rules 1 Answer Konstantinos Michailidis Nov 22, 2015 We have #f(x)=sinx^cosx# we can write this using logarithms as #f(x)=e^(cosx*lnsinx)# hence its first derivative is #(df(x))/dx=e^(cosx*lnsinx)*[(-sinx)*lnsinx+cosx*(cosx)/(sinx)]# or #(df(x))/dx=sinx^cosx*[cos^2x/sinx-sinx*lnsinx]# Answer link Related questions What is a summary of Differentiation Rules? What are the first three derivatives of #(xcos(x)-sin(x))/(x^2)#? How do you find the derivative of #(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))#? How do I find the derivative of #y= x arctan (2x) - (ln (1+4x^2))/4#? How do you find the derivative of #y = s/3 + 5s#? What is the second derivative of #(f * g)(x)# if f and g are functions such that #f'(x)=g(x)#... How do you calculate the derivative for #g(t)= 7/sqrtt#? Can you use a calculator to differentiate #f(x) = 3x^2 + 12#? What is the derivative of #ln(x)+ 3 ln(x) + 5/7x +(2/x)#? How do you find the formula for the derivative of #1/x#? See all questions in Summary of Differentiation Rules Impact of this question 1420 views around the world You can reuse this answer Creative Commons License