Product Rule Differentiation Example

00:00 3 marks

Differentiate the function $ f(x) = (3x^2 + 2x)(\sin x) $ with respect to $x$ using the product rule.

Hint Hint

Hint

Recall that the product rule is given by $ (u\cdot v)’ = u’v + uv’ $. Identify $u(x) = 3x^2 + 2x$ and $v(x) = \sin x$ accordingly.

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Answer Answer

Complete Answer

$ f'(x) = (6x + 2)\sin x + (3x^2 + 2x)\cos x $

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