Discussion

Let g(x)=sin(2x²+x) than g'(x) will be

Answer: B

Apply the chain rule to \( g(x) = \sin(2x^{2}+x) \).

\[ \frac{d}{dx}\sin u = \cos u \cdot \frac{du}{dx} \]

With \( u = 2x^{2}+x \):

\[ \frac{du}{dx} = 4x + 1 \]

\[ g'(x) = (4x+1)\cos(2x^{2}+x) \]

The outer function changes from sine to cosine; leaving it as a sine is the error the distractors are built on.

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