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Question
Differentiate the following w.r.t.x:
`(2x^(3/2) - 3x^(4/3) - 5)^(5/2)`
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Solution
Let y = `(2x^(3/2) - 3x^(4/3) - 5)^(5/2)`
Differentiating w.r.t. x,we get
`"dy"/"dx" = "d"/"dx"(2x^(3/2) - 3x^(4/3) - 5)^(5/2)`
= `(5)/(2)(2x^(3/2) - 3x^(4/3) - 5)^(5/2 - 1) xx "d"/"dx"(2x^(3/2) - 3x^(4/3) - 5)`
= `(5)/(2)(2x^(3/2) - 3x^(4/3) - 5)^(3/2) xx (2 xx (3)/(2)x^(3/2 - 1) -3 xx 4/3x^(4/3 -1) - 0)`
= `(5)/(2)(2x^(3/2) - 3x^(4/3) - 5)^(3/2)(3x^(1/2) - 4x^(1/3))`
= `(5)/(2)(3sqrt(x) - 4 root(3)(x))(2x^(3/2) - 3x^(4/3) - 5)^(3/2)`.
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