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a. If $f(x)=\frac{1}{3}\left(e^{3 x}+e^{-3 x}\right),$ calculate $f^{\prime}(1)$.

b. If $f(x)=e^{-\left(\frac{1}{a+1}\right)},$ calculate $f^{\prime}(0)$.

c. If $h(z)=z^{2}\left(1+e^{-z}\right),$ calculate $h^{\prime}(-1)$.

a. $e^{3}-e^{-3}$

b. $\frac{1}{e}$

c. $-2-3 e$

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{'transcript': "Hello, everyone. I hope all is well today. I'll be helping you with the six problem of the model four test. So this question is asking if f of x equals x minus one over X, then f of a plus f of one over a equals. What? So we just have to think through this problem and, uh, think about it in a way that they want us to. So, for example, so we have f of a equals a minus one over ace, We're plugging in a in this instance. So then if we have, um and then if we have f one over A, we would get one over a AA minus a. Alright. Ah, and then therefore f of a plus F one over a would equal zero because, um, thes cancel out because when you'd have a minus one over a and we add it to one over a minus A. This crosses out with here, and this crosses that with that. So you get zero, which is a so I hope you find the shovel. And I would be of a great day"}

University of California - San Diego

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