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

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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! 

Joseph  E. GCSE Maths tutor, A Level Maths tutor

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