WebAug 18, 2024 · Example \PageIndex {1}: Derivative of an Exponential Function Find the derivative of f (x)=e^ {\tan (2x)}. Solution: Using the derivative formula and the chain rule, f′ (x)=e^ {\tan (2x)}\frac {d} {dx} (\tan (2x))=e^ {\tan (2x)}\sec^2 (2x)⋅2 \nonumber Example \PageIndex {2}: Combining Differentiation Rules WebHere, f(x) = e 2x is an exponential function as the base is 'e' is a constant (which is known as Euler's number and its value is approximately 2.718) and the limit formula of 'e' is lim ₙ→∞ (1 + (1/n)) n. We can do the differentiation of e 2x in different methods such as: Using the first principle; Using the chain rule; Using logarithmic ...
Numerical differentiation by the polynomial-exponential basis
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How to Differentiate Exponential Functions – …
WebAug 18, 2016 · So we've already seen that the derivative with respect to x of e to the x is equal to e to x, which is a pretty amazing thing. One of the many things that makes e somewhat special. Though when you have an exponential with your base right over here as … WebDec 20, 2024 · Logarithmic differentiation allows us to differentiate functions of the form \(y=g(x)^{f(x)}\) or very complex functions by taking the natural logarithm of both sides and exploiting the properties of logarithms before differentiating. WebThe outer function is the exponential. Its derivative equals itslef. The inner function is ax: The derivative of the outer function equals the original function That was simple. It may take a few more examples to get used to the fact that the derivative of an exponential is the same exponential. Example 2: f (x) = ex2 cpu i7-8665u