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Question
If y = `root(5)((3x^2 + 8x + 5)^4)`, find `dy/dx`.
Sum
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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
`dy/dx = d/dx [(3x^2 + 8x + 5)^(4/5)]`
`= 4/5(3x^2 + 8x + 5)^(-1/5) * d/dx (3x^2 + 8x + 5)`
`= 4/5(3x^2 + 8x + 5)^(-1/5) * [3(2x) + 8 + 0]`
∴ `dy/dx = 4/5(3x^2 + 8x + 5)^(-1/5) * (6x + 8)`
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