Find the derivative of $y = x^2 \sin x$.
A$2x \sin x + x^2 \cos x$CORRECT
B$2x \cos x$
C$x^2 \cos x + 2x$
D$2x \sin x - x^2 \cos x$
GCEFurther MathematicsDifferentiation2024
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Why the answer is A, and why the others tempt you.
Using the product rule: dy/dx = (2x)(sin x) + (x²)(cos x) = 2x sin x + x² cos x. Option B incorrectly differentiates as if the product rule reduces to just multiplying derivatives. Option D has a sign error on the second term, and C omits the sin x factor from the first term.
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