Maharashtra State BoardHSC Commerce 12th Board Exam
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Find dydx, if y = (6x3 – 3x2 – 9x)10 - Mathematics and Statistics

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Sum

Find `("d"y)/("d"x)`, if y = (6x3 – 3x2 – 9x)10 

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Solution

y = (6x3 – 3x2 – 9x)10 

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

`("d"y)/("d"x) = "d"/("d"x)[(6x^3 - 3x^2 - 9x)^10]`

= `10(6x^3 - 3x^2 - 9x)^9 xx "d"/("d"x) (6x^3 - 3x^2 - 9x)`

= 10(6x3 − 3x2 − 9x)9 × [6(3x2) – 3(2x) − 9]

∴ `("d"y)/("d"x)` = = 10(6x3 − 3x2 − 9x)9 . (18x2 − 6x − 9)

Concept: Derivatives of Composite Functions - Chain Rule
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