Find $\dfrac{dy}{dx}$ if $y = \sin 3x$.
A$3\sin 3x$
B$-3\cos 3x$
C$\cos 3x$
D$3\cos 3x$CORRECT
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Why the answer is D, and why the others tempt you.
By the chain rule, the derivative of $\sin(3x)$ is $\cos(3x)$ multiplied by the derivative of $3x$, which is 3, giving $3\cos 3x$. Omitting the factor 3 or introducing a negative sign (which belongs to the derivative of cosine, not sine) gives the wrong results.
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