How do you differentiate f(x)=ln(1/sin(3x)) using the chain rule? Calculus Basic Differentiation Rules Chain Rule 1 Answer Sasha P. Nov 15, 2015 f'(x)= -3cot3x Explanation: f'(x)=(ln(1/(sin3x)))'=1/((1/(sin3x))) * (1/(sin3x))' f'(x)=sin3x * ((sin3x)^-1)' = sin3x * (-1)(sin3x)^-2 * (sin3x)' f'(x)=-sin3x * 1/(sin3x)^2 * cos3x * (3x)' f'(x)=-1/(sin3x) * cos3x * 3 f'(x)= -3cot3x 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 2654 views around the world You can reuse this answer Creative Commons License