How do you differentiate y = sin (ln(x)^2+2) using the chain rule? Calculus Basic Differentiation Rules Chain Rule 1 Answer maganbhai P. Jul 30, 2018 (dy)/(dx)=2/xlnx cos(ln(x)^2+2) Explanation: Here , y=sin(ln(x)^2+2) Let , y=sinu , where, color(red)(u=ln(x)^2+2 =>(dy)/(du)=cosu and (du)/(dx)=2lnx*1/x=2/xlnx Using Chain Rule: color(blue)((dy)/(dx)=(dy)/(du)*(du)/(dx) :.(dy)/(dx)=cosu xx 2/xlnx=2/xlnxcosu Subst. color(red)(u=ln(x)^2+2 :.(dy)/(dx)=2/xlnx cos(ln(x)^2+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 3967 views around the world You can reuse this answer Creative Commons License