nth Derivative of sinax bSolution1st derivative acosaxb 2n

n^th Derivative of sin(ax + b)|:-

1st derivative = a*cos(ax+b)

2nd derivative = -a^2 *sin(ax+b)

3rd derivative = -a^3 *cos(ax+b)

4th derivative = a^4 *sin(ax+b)

Thus,

nth derivative = a^n F(ax+b) where,

F(x) = sin x if x = 4k

F(x) = cos x if x = 4k+1

F(x) = -sin x if x = 4k+2

F(x) = -cos x if x = 4k+3