Why is the derivative of e^x the same as e^x? : r/askscience - Reddit
2014年8月6日 · If we derive this : exp'(x) * 1/exp(x) = 1 since the derivative of ln() is 1/x (this is how ln is defined by the way) the equation we got gives us exp'(x) = exp(x) for all x tl;dr: alternative way is from 1/x you define ln(x) then you define …
Can someone please explain why the derivitive of e^x is e^x
2021年5月11日 · First, let's not examine the derivative of e x, let's examine the derivative of a x, for all positive a. (a x+h-a x)/h = a x (a h-1)/h, which tells us that for all exponential functions, their derivative is proportionate to the original functions. That is, they fulfill the relationship f'(x)=g(a)f(x), where g(a) is some number that, as you ...
ELI5: why is the derivative of e^x also e^x? : r/explainlikeimfive
2021年10月20日 · The derivative of 2 x is ~0.7*2 x, so lightly smaller than the original function, the derivative of 3 x is ~1.1*3 x so slightly larger than the original function. This means that between 2 and 3 there must be some number which when used as the base, the derivative gives you the original value back.
Derivative of e^(xy) with respect to x : r/learnmath - Reddit
2023年9月14日 · the derivative of e xy with respect to x is ye xy. This is the correct partial derivative, yes. For partial derivatives we assume any other letter, including y, is constant, so d/dx [ e 4x] = e 4x · 4 d/dx [ e-1287.6 x] = -1287.6 e-1287.6 x. d/dx [ e x · √5] = √5 e x √5. are all done the same way that ∂/∂x [ e xy] = y e xy. is done.
Integrating e^(x^2) : r/learnmath - Reddit
2020年7月25日 · The chain rule is only applicable for differentiation; the antiderivative analogue is the u-substitution. You can’t perform it because the derivative of x 2 is not a factor of the integrand. On the other hand, the antiderivative of xe x^2 can easily be evaluated using u-substitution. e x^2 does not admit an elementary antiderivative. A ...
How come only e^x has the derivative be itself when using the
2022年10月20日 · This is a less intuitive answer but still a valid reply. The derivative of a function a x is a x •ln(a). Therefore; the derivative of 2 x is 2 x •ln(2). And so the derivative of e x is e x •ln(e). But ln(e) = 1, so you’re just left with e x
[High school maths?]Why can't you integrate e^(x^2) using the
2016年2月11日 · Well, no problem there, because we know that e u is its own derivative, so it's also its own antiderivative. Unfortunately there's more to it than that. We also have to change the variable of the differential, dx. We now have to have a du in the integral, not dx. This is done by saying, if: u = x 2. then: du/dx = 2x so: du = 2x dx
Any other functions than e^x and 0 that are derivatives of ... - Reddit
2012年3月19日 · My understanding was that e was discovered through its relation to the natural log function ln, which was invented as the integral of 1/x. Is it a coincidence then that ke x is the unique function that is the derivative of itself? Or is there some way to prove, from the definition of ln as the integral of 1/x, that the derivative of ke x is ke x?
[High School Math] Why is sinh(x) equal to (e^x-e^-x)/2
2018年3月19日 · A definition is a definition--sinh(x) is just the name we gave to the function (e x - e-x)/2. The way to understand a definition is to figure out why sinh(x) is defined the way it is, and why it's a useful definition. To first understand why it's useful to give this function a name, we should look at why it's useful to define cos(θ) and sin(θ).
Why there is no elementary antiderivative of exp(x^2) : r/math
Thank you. It's shocking me how many posts in this thread are saying that e x^2 isn't integrable. Actually I think the best part of this question is to teach Calc I students that being able to write down an indefinite integral in terms of 'elementary' functions is not the same thing as a function being integrable.