🎉 Announcing Numerade's $26M Series A, led by IDG Capital!Read how Numerade will revolutionize STEM Learning Oh no! Our educators are currently working hard solving this question. In the meantime, our AI Tutor recommends this similar expert step-by-step video covering the same topics. Numerade Educator ### Problem 4 Easy Difficulty # a. If$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)$. ### Answer ## a.$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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