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So to find the original function, we want to think about
what gives us out a derivative of cosine.
The answer is sine.
But then we need to do the division by the derivative of
the three T because we're trying to undo the chain rule.
So with the chain rule, we take the derivative of the inside and
multiply.
So to undo it, we're going to take the derivative of the
inside and divide.
We want to think about what gives us out a derivative for
sine, and the answer is negative cosine.
But then we need to take the divide by the derivative of the
inside plus some constant C So the derivative of 3T is 3 and
the derivative of t / 5 is 1/5.
When we simplify this up, we get 1/3 sine three t - 5 cosine t /
5 + C.