Asked by NONO
find d^85y/dx85 if y = sin x ??
I want the final rule because the solution will be repeated and therefore there will be a particular rule?
I want the final rule because the solution will be repeated and therefore there will be a particular rule?
Answers
Answered by
Steve
If y = sin x
dy/dx = cos x
d<sup>2</sup>y/dx<sup>2</sup> = -sin x
d<sup>3</sup>y/dx<sup>3</sup> = -cos x
d<sup>4</sup>y/dx<sup>4</sup> = sin x
...
d<sup>4k</sup>y/dx<sup>4k</sup> = sin x
d<sup>4k+1</sup>y/dx<sup>4k</sup> = cos x
d<sup>4k+2</sup>y/dx<sup>4k</sup> = -sin x
d<sup>4k+3</sup>y/dx<sup>4k</sup> = -cos x
dy/dx = cos x
d<sup>2</sup>y/dx<sup>2</sup> = -sin x
d<sup>3</sup>y/dx<sup>3</sup> = -cos x
d<sup>4</sup>y/dx<sup>4</sup> = sin x
...
d<sup>4k</sup>y/dx<sup>4k</sup> = sin x
d<sup>4k+1</sup>y/dx<sup>4k</sup> = cos x
d<sup>4k+2</sup>y/dx<sup>4k</sup> = -sin x
d<sup>4k+3</sup>y/dx<sup>4k</sup> = -cos x
Answered by
Steve
small typo. Should be dx<sup>4k+1</sup> etc.
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