Question

please help me everyone . what is the derivative of:
f(t)=20[1-cos^2(t/1000pi)]

Answer 1

20 is a constant and can be factored out.
derivative of 1 is zero
for derivative of:
\[\cos^2(\frac{ t }{ 1000 \pi })\]
use chain rule.
first use the property:
\[\frac{ d }{ dx }a^n = na^{n-1}\]
where a is 'a' constant and 'n' is some numerical value. 'a' can also be some function treated as a constant. For instance,
\[\frac{ d }{ dx }\sin^2(x) = 2\sin^{2-1}(x) \cos(x)\]
the cos(x) is just the derivative of the inside function (chain rule).