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!
JE
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