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Question
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)`
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)`
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