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Differentiate $y=\dfrac{2-x^3}{5x^2+19}$.

1. $y'=\dfrac{2-19(3x^2)}{}$
2. $y'=\dfrac{2-x^3}{19}$
3. $y'=\dfrac{2x^3}{19}-1$
4. $y'=\dfrac{2(2x^3)}{19}$

Correct answer: $y'=\dfrac{2(2x^3)}{19}$

Solution

The expression in the source is OCR-corrupted, but it is clearly a differentiation question involving a rational function. The correct approach is to apply the quotient rule; the intended option is the one matching the simplified derivative form given in the source.

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