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Free derivative calculator - differentiate functions with all the steps. Type in any function derivative to get the solution, steps and graph.
- First Derivative
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- Second Derivative
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- Indefinite Integrals
The derivative of the constant term of the given function is...
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- Derivative at a Point
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- Derivative Applications
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- First Derivative
The derivative of exponential function f (x) = a x, a > 0 is the product of exponential function a x and natural log of a, that is, f' (x) = a x ln a. Mathematically, the derivative of exponential function is written as d (a x)/dx = (a x)' = a x ln a.
Find the derivative of \(f(x) = xe^x\sin x.\) Let \(u(x) = x, v(x) = e^x,\) and \(w(x) = \sin x\) so that \(f(x) = u(x)v(x)w(x)\). Then \(u'(x) = 1, v'(x) = e^x, w'(x) = \cos x.\)
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.
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.
