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20 Νοε 2021 · The first of these is the exponential function. Let \(a \gt 0\) and set \(f(x) = a^x\) — this is what is known as an exponential function. Let's see what happens when we try to compute the derivative of this function just using the definition of the derivative.
In order to differentiate the exponential function \[f(x) = a^x,\] we cannot use power rule as we require the exponent to be a fixed number and the base to be a variable. Instead, we're going to have to start with the definition of the derivative:
27 Φεβ 2018 · This calculus video tutorial explains how to find the derivative of exponential functions using a simple formula. It explains how to do so with the natural base e or with any other number....
17 Αυγ 2024 · Find the derivative of exponential functions. Find the derivative of logarithmic functions. Use logarithmic differentiation to determine the derivative of a function.
To differentiate an exponential function, copy the exponential function and multiply it by the derivative of the power. For example, to differentiate f(x)=e 2x , take the function of e 2x and multiply it by the derivative of the power, 2x.
21 Ιουν 2023 · Using the definition of the derivative, calculate the derivative of the function \(y=a^{x}\) for an arbitrary base \(a>0\). Describe the significance of the special base \(e\). Summarize the properties of the function \(e^{x}\), its derivatives, and how to manipulate it algebraically.
