Maharashtra State BoardHSC Commerce 12th Board Exam
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Find dydx, if y = (3x2+x+5)45 - Mathematics and Statistics

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Sum

Find `("d"y)/("d"x)`, if y = `root(5)((3x^2 + 8x + 5)^4`

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Solution

y = `root(5)((3x^2 + 8x + 5)^4`

y = `(3x^2 + 8x + 5)^(4/5)`

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

`("d"y)/("d"x) = "d"/("d"x) [(3x^2 + 8x + 5)^(4/5)]`

= `4/5(3x^2 + 8x + 5)^(-1/5)*"d"/("d"x)(3x^2 + 8x + 5)`

= `4/5(3x^2 + 8x + 5)^(-1/5)*[3(2x) + 8 + 0]`

∴ `("d"y)/("d"x) = 4/5(3x^2 + 8x + 5)^(1/5)*(6x + 8)`

Concept: Derivatives of Composite Functions - Chain Rule
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