Question

please help me. ACTUALLY. What is the derivative of:
f(t)=20[1-cos^29t/1000pi)] PLEEEASE

Answer 1

write it correctly first. theres no such thing as cos^29t

Answer 2

cos^2(t/1000pi)
i guess i didnt hit shift when I hit 9.

Answer 3

\[f(t) = 20 - 20 \cos(\frac{t}{1000\pi})\]
the derivative of cos(x) is -sin(x), the derivative of 20 is 0, so
\[f'(t) = 0 - (-20\sin(\frac{t}{1000\pi}) \frac{1}{1000\pi})\]
where 1/1000pi is the derivative of t/1000 pi (chain rule!). So the result is
\[f'(t) =\frac{1}{50\pi}\sin(\frac{t}{1000\pi}) \]