Question

Choose the correct alternative.

If y = (5x³ - 4x² - 8x)⁹, then `"dy"/"dx"` =

Options

• 9(5x³ - 4x² - 8x)⁸ (15x² - 8x - 8)

• 9(5x³ - 4x² - 8x)⁹ (15x² - 8x - 8)

• 9(5x³ - 4x² - 8x)⁸ (5x² - 8x - 8)

• 9(5x³ - 4x² - 8x)⁹ (15x² - 8x - 8)

Answer 1

9(5x³ - 4x² - 8x)⁸ (15x² - 8x - 8)

Explanation:

y = (5x³ - 4x² - 8x)⁹ 

Differentiating both sides w.r.t.x, we get

`"dy"/"dx" = "d"/"dx"` [(5x³ - 4x² - 8x)⁹]

`= 9("5x"^3 - 4"x"^2 - 8"x")^8 * "d"/"dx" ("5x"^3 - 4"x"^2 - 8"x")`

`= 9("5x"^3 - 4"x"^2 - 8"x")^8 * [5(3"x"^2) - 4(2"x") - 8]`

∴ `"dy"/"dx" = 9("5x"^3 - 4"x"^2 - 8"x")^8 * (15"x"^2 - 8"x" - 8)`