Question

to find nth derivative of x/(x square +a square)

Answer 1

answer is The answer for first order derivative will be :

n∗(x2–1)(n−1)∗2xn∗(x2–1)(n−1)∗2x

while doing second time don’t consider “n” as it is free from x. The answer will be :

n∗(x2–1)(n−1)∗2+2x∗(n−1)∗(x2−1)(n−2)∗

or
pm=n!(n−m)!=n(n−1)(n−2)...(n−m+1)pm=n!(n−m)!=n(n−1)(n−2)...(n−m+1)

and cm=n!m!(n−m)!cm=n!m!(n−m)!for eachm=1,2,..n.m=1,2,..n.

Therefore cm.m!=pm.cm.m!=pm.

By Leibnitz theorem for the nth derivative of product of two functions, we get

(uv)(n)=u(n)v(uv)(n)=u(n)v

+c1.u(n−1)v(1)+c1.u(n−1)v(1)

+c2.u(n−2)v(2)+...+u.v(n)+c2.u(n−2)v(2)+...+u.v(n)

……………………………………….. . (1)

Taking u=(x+1)nv=(x−1)nu=(x+1)nv=(x−1)n

in (1) we get

(x2−1)n)(n)=(n!).(x−1)n(x2−1)n)(n)=(n!).(x−1)n

+c1.pn−1.(x+1)1.p1.(x−1)n−1+c1.pn−1.(x+1)1.p1.(x−1)n−1

+c2.pn−2.(x+1)2.p2.(x−1)n−2+...+(x+1)n.(n!)+c2.pn−2.(x+1)2.p2.(x−1)n−2+...+(x+1)n.(n!) plz mark as brainliest