Question

find d^999/dx^999(cosx)

step by step​

Answer 1

Answer:

HEY MATE HERE'S YOUR ANSWER....

[[d^2 / dx^2] cos x = [d / dx] [d / dx] cos x = [d / dx] (- sin x) = - cos x[d^3 / dx^3] cos x = [d / dx] [d^2 / dx^2] cos x = [d / dx] (- cos x) = sin x[d^4 / dx^4] cos x = [d / dx] [d^3 / dx^3] cos x = [d / dx] sin x = cos xnow we see that [d^4 / dx^4] cos x = cos x. in other words, if we take the derivative 4 times, it comes back to cos x. now we'll take the derivative 996 = 249x4 times and it will again be cos x.[d^996 / dx^996] cos x = [d^4 / dx^4] [d^4 / dx^4] ... [d^4 / dx^4] cos x = cos xnow we take the derivative 3 more times to get the answer.[d^999 / dx^999] cos x = [d^3 / dx^3] [d^996 / dx^996] cos x =[d^3 / dx^3] cos x = sin x

thus the answer is[d^999 / dx^999] cos x = sin x...

HOPE THIS ANSWER HELPFUL TO YOU....