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What is the nth derivative of 1/x?

2 Answers

7 votes

Final answer:

The nth derivative of 1/x can be found using the power rule for differentiation.

Step-by-step explanation:

The nth derivative of 1/x can be found using the power rule for differentiation. The power rule states that if you have a function f(x) = x^n, then the nth derivative of f(x) is given by:

f(n)(x) = n(n-1)(n-2)...(n-(n-1))x^(n-n)

For 1/x, the function can be rewritten as x^(-1). Applying the power rule, we get:

f'(x) = (-1)(-1 - 1)x^(-1 - 2) = 2x^(-3)

So, the nth derivative of 1/x is given by f(n)(x) = n!x^(-n-1).

User Salmen Bejaoui
by
3.0k points
2 votes

Answer:

(-1)^n × (n!) × x^-(n+1)

Step-by-step explanation:

I've attached the solution

What is the nth derivative of 1/x?-example-1
User Dreen
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3.6k points