Given the piecewise function: f(x)={(6tan(x), if 0<=x<(π)/(2)),(8cot(x), if (π)/(2)<=x<π):}, what is the value of f^'((π)/(4))+f^'((3π)/(4))?

A) 12tan((π)/(4))+16cot((3π)/(4))
B) 6tan((π)/(4))+8cot((3π)/(4))
C) 12tan((π)/(4))+8cot((3π)/(4))
D) 6tan((π)/(4))+16cot((3π)/(4))