Differentiate y=(4x - 5)^5 by using the chain rule.

Notation: I use the ^ in the title question to indicated 'to the power of' and I use an asterisk * (or star) to indicate 'multiplied by' in the answer, to avoid confusion with the x term! 

Step 1) let u = 4x - 5      therefore y = u⁵

Step 2) du/dx = 4           dy/du = 5u⁴

Step 3) (the chain rule!)  dy/dx = dy/du * du/dx

so dy/dx = 5u⁴ * 4

     dy/dx = 20u⁴ 

     dy/dx = 20(4x - 5)⁴ as we substitute for the u term to complete our answer!