Question

what is the derivative of cos(pi*t/4)

Answer 1

sin(pi*t/4) * pi/4

Answer 2

-sin(pi*t/4)(pi/4)

Answer 3

negative!!!!!

Answer 4

why would it be times (pi/4) for second term

Answer 5

\[f(x)=\cos(\pi t/4)\]chain rule:
derivative of f(g(x))=f'(g(x))g'(x)
here f(x)=cos(pi*t/4) and g(x)=(pi/4)t
so g'(x)=pi/4\[f'(x)=-\sin (\pi t/4)(\pi/4)=-(\pi/4)\sin (\pi t/4)\]