Calc 1 Pauls Online Notes Jun 2026

Example: Differentiate ( f(x) = \sin(x^2) ). Step 1: Identify the outer function (( \sin(u) )) and inner function (( u = x^2 )). Step 2: Derivative of outer: ( \cos(u) ). Step 3: Derivative of inner: ( 2x ). Step 4: Multiply: ( \cos(x^2) \cdot 2x ). Final: ( 2x \cos(x^2) ).

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