Calc 1, Lec 11B: Derivatives of Exponential Functions, Mass on a Spring, Derivative of Cosine

The most important special fact in Calculus is the easiest to remember! THe derivative of e^x is e^x (that is, (e^x)'=e^x). We can derive this with the limit definition of the derivative (and computing help). We can also verify, with the help of technology, that (b^x)'=ln(b)*b^x. We can also make sense of these facts graphically. A mass on a spring can be modeled with a sinusoidal function, such as cosine cos(t). The derivative of cosine is negative sine: (cos(t))'=-sin(t).

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