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