If Y = X³(5 + X ²)⁴,then dY/dX is: A) 3X ²(5 + X ²)⁴ + 8X³(5 + X ²)³. B) 3X ²(5 + X ²)⁴ + 8X⁴(X ²)³. C) 3X ²(5 + X ²)³. D) 3X ²(5 + X ²)⁴ + 8X⁴(5 + X ²)³. E) 3X ²(5 + X ²)⁴ + 8X⁴(5 + X ²)².

Question

Quizplus · Accepted Answer

Using the chain rule, we have: dY/dX = (5 + X ²)^³ * d/dX (X ²)^⁴ + Y * d/dX (5 + X ²)^³ Applying the product rule on the first term and the chain rule on the second term: dY/dX = (5 + X ²)^³ * ⁴ * (X ²)^³-1 * d/dX (X ²) + Y * ³ * (5 + X ²)^³-1 * ² Simplifying and factoring: dY/dX = 3X ²(5 + X ²)⁴ + 8X³(5 + X ²)⁴

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