Question

What is the derivative of `5 cos^2 pi t`?

Answer 1

=`-10 pi cos(pi t) sin (pi t)`

Explanation:

1. hope you can read the notation :)
2. deriv .. put in form `5 (cos ( pi t))^2`
3. power rule first gets `10 ( cos (pi t))`
4. chain rule requires that you multiply by the deriv of the inside function. `d/dt ( cos ( pi t)) = - sin ( pi t) * pi`
5. the last multiply by pi is due to the chain rule applied to ( pi t)