Question

find the nth derivative of y=x/x^2+a^2
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Answer 1

Step-by-step explanation:

The function can be re-written as y = x(x^2 + a^2)^-1.

The 1st derivative, using the product rule is:

x*-1(x^2 + a^2)^-2 * 2x + (x^2 + a^2)^-1

Which can be simplified as:

-2x^2(x^2 + a^2)^-2 + (x^2 + a^2)^-1

The 2nd derivative is:

-2x^2 * -2(x^2 + a^2)^-3 * 2x + (x^2 + a^2)^-2 * -4x

Which simplifies to:

8x^3(x^2 + a^2)^-3 - 4x(x^2 + a^2)^-2

Keep doing this to see if a pattern emerges.