Transformation to the second and third derivative?

Hello,

cannot fully understand the step from the first to the second derivative, and even less so from the second to the third.

It would be cool if someone could show me how to calculate it.

Merce

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Prism97
2 months ago

First, re-form the fracture:

And then apply the product rule. Do not forget the internal derivation of the clamp.

Prism97
2 months ago
Reply to  eshatgrad8uhr

If you understand, you can also do the other derivation. Just the same principle. Forming and product rule, otherwise you should not need anything. Just become very long and annoying terms.

Rammstein53
2 months ago

Partial breaking down:

Forming:

Now the discharges can be easily determined with the potency rule:

Even if you do not recognize it right away, this solution is identical to the solution in your question.

gauss58
2 months ago

f(x) = x / (x2 – 4)

f'(x) = (1 * (x2 – 4) – 2 * x * x) / (x2 – 4)2

f'(x) = (1 * (x2 – 4) / (x2 – 4)2) – 2 * x2 / (x2 – 4)2

f'(x) = (1 / (x2 – 4)) – 2 * x2 / (x2 – 4)2

f”'(x) = (- 2 * x * 1) / (x2 – 4)2 – ((4 * x * (x2 – 4)2 – 2 * (x2 – 4) * 2 * x * 2 * x2) / (x2 – 4)4)

f”'(x) = (-2 * x / (x2 – 4)2) – (4 * x * (x2 – 4)2 – 8 * x3 * (x2 – 4)) / (x2 – 4)4)

f”'(x) = (-2 * x / (x2 – 4)2) – ((4 * x / (x2 – 4)2) – 8 * x3) / (x2 – 4)3)

f”'(x) = (8 * x3 / (x2 – 4)3) – 6 * x / (x2 – 4)2

f””(x) = ((24 * x2 * (x2 – 4)3 – 3 * (x2 – 4)2 * 2 * x * 8 * x3) / (x2 – 4)6) –

(6 * (x2 – 4)2 – 2 * (x2 – 4) * 2 * x * 6 * x) / (x2 – 4)4

f””(x) = (24 * x2 / (x2 – 4)3) – (48 * x4 / (x2 – 4)4) – ((6 / (x2 – 4)2) – 24 * x2 / (x2 – 4)3)

f””(x) = (-6 / (x2 – 4)2) + (24 * x2 / (x2 – 4)3) + (24 * x2 / (x2 – 4)3) – 48 * x4 / (x2 – 4)4)

f””(x) = (-6 / (x2 – 4)2) + (48 * x2 / (x2 – 4)3) – (48 * x4 / (x2 – 4)4)4)