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Question
Find the second order derivatives of the following : `2x^5 - 4x^3 - (2)/x^2 - 9`
Solution
Let y = `2x^5 - 4x^3 - (2)/x^2 - 9`
Then `"dy"/"dx" = "d"/"dx"(2x^5 - 4x^3 - 2/x^2 - 9)`
= `2"d"/"dx"(x^5) - 4"d"/"dx"(x^3) - 2"d"/"dx"(x^-2) - "d"/"dx"(9)`
= 2 x 5x4 – 4 x 3x2 – 2(–2)x–3 – 0
= 10x4 – 12x2 + 4x–3
and
`(d^2y)/(dx^2) = "d"/"dx"(10x^4 - 12x^2 + 4x^-3)`
= `10"d"/"dx"(x^4) - 12"d"/"dx"(x^2) + 4"d"/"dx"(x^-3)`
= 10 x 4x3 – 12 x 2x + 4(–3)x–4
= `40x^3 - 24x - (12)/x^4`.
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