Maharashtra State BoardHSC Commerce 12th Board Exam
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Y = (6x4 – 5x3 + 2x + 3)6, find dydx Solution: Given, y = (6x4 – 5x3 + 2x + 3)6 Let u = [6x4-5x3+□+3] ∴ y = u□ ∴ dydu = 6u6–1 ∴ dydu = 6( )5 and dudx=24x3-15(□)+2 By chain rule, dydx=dy□×□dx ∴ - Mathematics and Statistics

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Sum

y = (6x4 – 5x3 + 2x + 3)6, find `("d"y)/("d"x)`

Solution: Given,

y = (6x4 – 5x3 + 2x + 3)6 

Let u = `[6x^4 - 5x^3 + square + 3]`

∴ y = `"u"^square`

∴ `("d"y)/"du"` = 6u6–1

∴ `("d"y)/"du"` = 6(  )5 

and `"du"/("d"x) = 24x^3 - 15(square) + 2`

By chain rule,

`("d"y)/("d"x) = ("d"y)/square xx square/("d"x)`

∴ `("d"y)/("d"x) = 6(6x^4 - 5x^3 + 2x + 3)^square xx (24x^3 - 15x^2 + square)`

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Solution

Given,

y = (6x4 – 5x3 + 2x + 3)6 

Let u = [6x4 – 5x3 + 2x + 3]

∴ y = `"u"^6`

∴ `("d"y)/"du"` = 6u6–1

∴ `("d"y)/"du"` = 6(u)5 

and `"du"/("d"x) = 24x^3 - 15x^2 + 2`

By chain rule,

`("d"y)/("d"x) = ("d"y)/"du" xx "du"/("d"x)`

∴ `("d"y)/("d"x) = 6(6x^4 - 5x^3 + 2x + 3)^5 xx (24x^3 - 15x^2 + 2)`

Concept: Derivatives of Composite Functions - Chain Rule
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