Continuity And Differentiability

Question

Use Chain rule to find the derivative of (3x² + 2)².

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Solution

Let y = f(x) = {3x² + 2)² = u² where u = 3x² + 2

therefore space dy over du equals 2 space straight u comma space du over dx equals 6 space straight x By space chain space rule comma space space space space space dy over dx equals dy over du du over dx equals left parenthesis 2 space straight u right parenthesis left parenthesis 6 space straight x right parenthesis equals 12 space straight x space straight u therefore space space dy over dx equals 12 space straight x left parenthesis 3 space straight x squared plus 2 right parenthesis