How do you use the chain rule to differentiate (sinx)^10? Calculus Basic Differentiation Rules Chain Rule 1 Answer Henry W. Nov 5, 2016 (dy)/(dx)=10sin^9xcosx Explanation: By treating (sinx)^10 as a function in terms of sinx, and sinx as a function in terms of x, chain rule can be applied where: (dy)/(dx)=(dy)/(du)*(du)/(dx) Let u=sinx :.y=u^10 (dy)/(du)=10u^9=10(sinx)^9 (du)/(dx)=cosx->the derivative of sinx is cosx :.(dy)/(dx)=10(sinx)^9*cosx=10sin^9xcosx 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 2857 views around the world You can reuse this answer Creative Commons License