find d^85y/dx85 if y = sin x ??

Question

I want the final rule because the solution will be repeated and therefore there will be a particular rule?

Answer 1

If y = sin x
dy/dx = cos x
d²y/dx² = -sin x
d³y/dx³ = -cos x
d⁴y/dx⁴ = sin x
...
d^4ky/dx^4k = sin x
d^4k+1y/dx^4k = cos x
d^4k+2y/dx^4k = -sin x
d^4k+3y/dx^4k = -cos x

Answer 2

small typo. Should be dx^4k+1 etc.