How do you differentiate #f(x)=sqrt(((3x)/(2x-3))# using the chain rule? Calculus Basic Differentiation Rules Chain Rule 1 Answer Sonnhard Jun 1, 2018 #f'(x)=-9/2*((3*x)/(2*x-3))^(-1/2)# Explanation: Writing #f(x)=((3*x)/(2x-3))^(1/2)# so we get #f'(x)=1/2*((3*x)/(2x-3))^(-1/2)*(3*(2x-3)-3x*2)/(2x-3)^2# so #f'(x)=-9/2*((3x)/(2x-3))^(-1/2)# 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 1445 views around the world You can reuse this answer Creative Commons License