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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)
Solution
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)`
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