E X Derivative Meme

First we take the derivative of the entire expression then we multiply it by the derivative of the expression in the exponent. The exponent rule is a more generalized version of the special rule for finding the derivative of e x. Frac text d text d x e x e x the chain rule.

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E x derivative meme. 157 points 1 year ago. To see the answer pass your mouse over the colored area. To cover the answer again click refresh reload. E sin x cos x. That is the slope of all line tangent to the graph e x is just e x. Of all functions f x e x is the only function whose derivative is itself. Now you can forget for a while the series expression for the exponential.

The important thing is that e x is a very special function because its the only one. All you need to know is that e x is something called a function and taking the derivative or d dx is something commonly done to functions that results in another altered function. Pimp my calculus. So not only is the slope of e x e x the area underneath the graph of e x is also e x. Keep on deriving. Do the problem yourself first. At the same time it s not though.

This is such a derivative meme. Let s just pick some points on this curve of y is equal to e to the x and think about what the slope of the tangent line is or what the derivative looks like and so let s say when y is equal to one or when e to the x is equal to one this is the case when x is equal to zero. Because at any point on e x the slope is equal to e x. E x 2 2x 2x e x 2. Differentiation of e x is e x. That s such an arbritrary number isn t it. If you don t understand this meme then chances are you re failing ap calculus.

When the exponential expression is something other than simply x we apply the chain rule. We only needed it here to prove the result above. E x 1 e x. There s no shortage of memes in 2017 and believe it when we say there are more to come. So we re gonna do a little bit of an exploration. We can now apply that to calculate the derivative of other functions involving the exponential. The derivative of e x is e x.

X 2 e x. Here is the image which explains it. Isn t it crazy how the derivative of e x is e x. Image conveys more information than a normal text. Calculate the derivative of the following. But at the same time the integral of e x is also e x. C x 2 e x.

A post shared by ap calculus memes apcalcmemes on nov 21 2016 at 5 31pm pst. Calculate the derivative of e x 2. This is one of the properties that makes the exponential function really important. As i have learned in my engineering.