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y=(x-1)^(2)

$y=(x-1)^{2}$

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Find derivatives using the chain rule II

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Q.

y=(x-1)^{2}

Identify Function and Rule: Identify the function and the rule needed for differentiation. $\newline$ We have $y = (x-1)^2$ , which is a basic power function. $\newline$ Using the power rule for differentiation, where if $y = u^n$ , then $y' = n\cdot u^{(n-1)}\cdot u'$ .
Differentiate Inside Function: Differentiate the inside function $u = x-1$ . Differentiating $u = x-1$ gives us $u' = 1$ .
Apply Chain Rule: Apply the chain rule. $\newline$ Using the power rule and the result from the previous step, the derivative $y' = 2\cdot(x-1)^{2-1}\cdot1$ . $\newline$ Simplify to get $y' = 2\cdot(x-1)$ .

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