How do you differentiate #y = x^5 + (7 − x)^5#? Calculus Basic Differentiation Rules Chain Rule 1 Answer Alan N. Apr 13, 2018 #dy/dx = 5(x^4-(7-x)^4)# Explanation: #y = x^5+(7-x)^5# Apply power rule and chain rule. #dy/dx= 5x^4 + 5(7-x)^4 * d/dx(7-x)# #= 5x^4+5(7-x)^4 * (0-1)# #= 5(x^4-(7-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 1750 views around the world You can reuse this answer Creative Commons License