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

Answer 1

Emily Ammerman

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

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

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Answer 2

Ezra Adams

The derivative of (5 \cos^2(\pi t)) with respect to (t) is (-10\pi \cos(\pi t) \sin(\pi t)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.