SOLUTION: Let f(x) = sin(ax + b) and let g(x)=cos(a+b) where a and b are constants. Guess a formular for f^n(x) and for g^n(x) general n (positive integer )

Question 1164540: Let f(x) = sin(ax + b) and let g(x)=cos(a+b) where a and b are
constants. Guess a formular for f^n(x) and for g^n(x) general n (positive
integer )
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

f(x) = sin(ax+b)
f'(x) = a*(cos(ax+b))
f(2)(x) = a^2*(-sin(ax+b))
f(3)(x) = a^3*(-cos(ax+b))
f(4)(x) = a^4*(sin(ax+b))
f(5)(x) = a^5*(cos(ax+b))
...

You can generalize that pattern however you want.

For g(x) = cos(ax+b), there would be a similar pattern in the derivatives, which you can determine based on the derivatives shown above for sin(ax+b).

However, the second part of your question shows g(x) = cos(a+b), which is a constant. So all the derivatives of g(x) are zero.

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