Question 1164540
<br>
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))
...<br>
You can generalize that pattern however you want.<br>
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).<br>
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.<br>