Question

Find the second order derivatives of the following : `2x^5 - 4x^3 - (2)/x^2 - 9`

Answer 1

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`.