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Determine the derivative.$f(x)=e^{a x^{2}}, a$ is a constant

$2 a x e^{a x^{2}}$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 4

The Derivative of the Exponential Function

Campbell University

Baylor University

University of Michigan - Ann Arbor

Lectures

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The main concept in this, uh, section is understanding the derivative of E to the X eso It's e to a function. But if you consider the change rule, then what you have to do is the derivative of that piece. Now, this first problem, you know, this one I'm looking at is basically just saying the drift of elevated The X is either the ex with the chain rule, so it will make more sense when I actually do a problem. So let's do the derivative of E to the A X square power. That's what we're supposed to do in this problem. So as we look at that of the derivative is the same thing e to the X squared. But then you have to multiply by the derivative of a X squared and you bring that to in front. The A is just a constant, so it stays there. X. So that's why our final answer in a lot of Matthew people will write it this way. Um, just make sure that you make your expose look like excellence, But this is all multiplication. Two times eight times x times e to the X square. Oh, yeah, yeah

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