How do you differentiate f(x)=e^tan(lnx) using the chain rule? Calculus Basic Differentiation Rules Chain Rule 1 Answer Sasha P. Oct 29, 2015 f'(x) = (e^(tan(lnx))sec^2(lnx))/x Explanation: f'(x) = (e^(tan(lnx)))' = e^(tan(lnx)) * (tan(lnx))' = e^(tan(lnx)) * sec^2(lnx) * (lnx)' = e^(tan(lnx)) * sec^2(lnx) * 1/x f'(x) = (e^(tan(lnx))sec^2(lnx))/x Answer link Related questions What is the Chain Rule for derivatives? How do you find the derivative of y= 6cos(x^2) ? How do you find the derivative of y=6 cos(x^3+3) ? How do you find the derivative of y=e^(x^2) ? How do you find the derivative of y=ln(sin(x)) ? How do you find the derivative of y=ln(e^x+3) ? How do you find the derivative of y=tan(5x) ? How do you find the derivative of y= (4x-x^2)^10 ? How do you find the derivative of y= (x^2+3x+5)^(1/4) ? How do you find the derivative of y= ((1+x)/(1-x))^3 ? See all questions in Chain Rule Impact of this question 1919 views around the world You can reuse this answer Creative Commons License