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 1474 views around the world You can reuse this answer Creative Commons License