dX) when x = 1.

150

175

195

Y = 4X3 - 6X2 + 15X – 19 and Z = 3X2 + 5X - 9. Find the value of (dY/dX) (dZ/dX) when x = 1. Correct Answer <span style="">165</span>

Given:

Y = 4X3 - 6X2 + 15X – 19

Z = 3X2 + 5X - 9

Concept:

If x = yⁿ, then differentiation is dx/dy = ny^{n - 1}

Calculation:

Y = 4X3 - 6X2 + 15X – 19

dy/dx = 12x² - 12x + 15 ---- (1)

Z = 3X2 + 5X - 9

dz/dx = 6x + 5 ---- (2)

(dy/dx) (dz/dx) = (12x² - 12x + 15) (6x + 5) (from 1 and 2)

⇒

⇒ 15 × 11

⇒ 165

∴ The value of (dY/dX) (dZ/dX) when x = 1 is 165.

Feb 20, 2025

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