How do you differentiate 2e x

What does this mean? It means the slope is the same as the function value the y -value for all points on the graph. If u is a function of x , we can obtain the derivative of an expression in the form e u :. If we have an exponential function with some base b , we have the following derivative:.

See the chapter on Exponential and Logarithmic Functions if you need a refresher on exponential functions before starting this section. Now, using the logarithm laws , we have:. We tidy this up by multiplying top and bottom by x. Also, it's best to write the 2 e 2 x in front of the logarithm expression to reduce confusion.

It's not part of the log expression. We'll see more of these curves in Second Order Differential Equations , in the later calculus section. Disclaimer: IntMath. Problem Solver provided by Mathway. Bio: Hi! I am Ligia, I really enjoy mentoring others and have worked as a math tutor at Stanford. I also interested in the physical sciences, and I do research using machine learning in biological problems.

It's the number e. The number e is an irrational number and therefore we can only give an approximate value for e, e 2. One of the results of this rule is that if x is multiplied by a constant number then the differentiated f unction is also multiplied by that constant.

Putting these values into the formula we get. Now we consider a rule often referred to as the sandwich rule. This is a method we can use to solve difficult limit problems. If we are unable to find the limit of a function f x in a particular point P we can try to find a function u x that has the same value as f x in the point P but is greater than f x in the neighbourhood of P.

In the same way we find a function v x that takes the same value as f x in the point P but is less than f x in the neighbourhood of P. In this way we sandwich f x in between u x and v x. If these two functions u x and v x have the same limit in point P then f x must also have this limit. This is demonstrated in the diagram below. Now we will use the sandwich rule to find. The above diagram shows the unit circle. Post as a guest Name. Email Required, but never shown. Upcoming Events.

Featured on Meta. Now live: A fully responsive profile. The unofficial elections nomination post. Related 3. Hot Network Questions.

Question feed. Mathematics Stack Exchange works best with JavaScript enabled. Accept all cookies Customize settings.