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Question
Solve the following:
If y = (6x3 - 3x2 - 9x)10, find `"dy"/"dx"`
Solution
y = (6x3 - 3x2 - 9x)10
Differentiating both sides w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"[(6"x"^3 - 3"x"^2 - 9"x")^10]`
`= 10(6"x"^3 - 3"x"^2 - 9"x")^9 xx "d"/"dx" (6"x"^3 - 3"x"^2 - 9"x")`
`= 10(6"x"^3 - 3"x"^2 - 9"x")^9 xx [6(3"x"^2) - 3("2x") - 9]`
∴ `"dy"/"dx" = 10(6"x"^3 - 3"x"^2 - 9"x")^9 * (18"x"^2 - 6"x" - 9)`
Notes
The answer in the textbook is incorrect.
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