differentiation of exponential functions question, please help (1 Viewer)
- Thread starter miracu
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davidgoes4wce
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Sorry to be a hassle, but the textbook I'm using only gives the answer and shows no working out or gives any similar examples. I get how you found f'(x) but how did you find f'(a) from that point? = \frac{a}{2} \left(e^{x/a} + e^{-x/a}\right)$ \\ Well $\frac{\textrm{d}}{\textrm{d}x}f(x) = \frac{a}{2}\left(\frac{1}{a} \cdot e^{x/a} - \frac{1}{a} \cdot e^{-x/a}\right) = \frac{1}{2}\left(e^{x/a} - e^{-x/a}\right).$ \\ Thus, $f'(a) = \frac{1}{2}\left(e-e^{-1}\right))
You substitute x = a into f'(x). The exponents simply become a/a = 1 and -a/a = -1