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Question
Differentiate the following:
y = `root(3)(1 + x^3)`
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Solution
y = `root(3)(1 + x^3)`
y = `(1 + x^3)^(1/3)`
[y = f(g(x)
`("d"y)/("d"x)` = f'(g(x)) . g'(x)]
`("d"y)/("d"x) = 1/3 (1 + x^3)^(1/3 - 1) xx "d"/("d"x) (1 + x^3)`
`("d"y)/("d"x) = 1/3 (1 + x^3)^(- 2/3) (0 + 3x^2)`
`("d"y)/("d"x) = 1/3 1/(1 + x^3)^(2/3) xx 3x^2`
`("d"y)/("d"x) = x^2/(1 + x^3)^(2/3)`
= `x^2 (1 + x^3)^(- 2/3)`
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