Calculus I Applications of Basic Derivatives 2. The Derivative of $e^x$ The graph of $e^x$ is provided for you below. Use your calculator to graph the derivative of $e^x$ using the definition of derivative $f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$, with $h = .0001$. $f(x) = e^x$ $f'(x)$ So, what is the derivative of $e^x$: _________ If you have time, find $\frac{dy}{dx}$: (a) $y = 2e^x + 2xe^x$ (b) $y = e^x - \cos x$ (c) $y = x^4 - \frac{\sin x}{6} + \frac{e^x}{3}$
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The derivative of a function represents the rate of change of that function at any given point. In this case, we want to find the derivative of the function e^x. Show more…
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