How do you find the derivative using the power chain rule of y=(cos(x^4)+x^3))^8? Calculus Basic Differentiation Rules Chain Rule 1 Answer bp Aug 10, 2015 8(cos x^4 +x^3)^7 *(3x^2 -4x^3 sin x^4) Explanation: dy/dx = 8 (cos x^4 +x^3)^7 d/dx (cos x^4 +x^3) = 8(cos x^4 +x^3)^7 * (d/dx cosx^4 +d/dx x^3) =8(cos x^4 +x^3)^7 *(-sin x^4 4x^3 +3x^2) =8(cos x^4 +x^3)^7 (3x^2 -4x^3 sin x^4) 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 1896 views around the world You can reuse this answer Creative Commons License