# Is ex a derivative? ### Is ex a derivative?

The derivative of ex is quite remarkable. The expression for the derivative is the same as the expression that we started with; that is, ex!

### What is ex differentiation?

Differentiation of f(x)=ex To differentiate y = ex we will rewrite this expression in its alternative form using logarithms: ln y = x Then differentiating both sides with respect to x, d dx (lny)=1 The idea is now to find dy dx .

### Which function is its own derivative and its own integral?

exponential function The exponential function, y=ex, is its own derivative and its own integral. Exponential functions can be integrated using the following formulas. Find the antiderivative of the exponential function e−x. Use substitution, setting u=−x, and then du=−1dx.

### How do I find out what my ex is worth?

In the ex function, the slope of the tangent line to any point on the graph is equal to its y-coordinate at that point. (1 + 1/n)ⁿ is the sequence that we use to estimate the value of e. The sequence gets closer to e the larger n is - but even if n = infinity, the sequence value is not equal to Euler's number.

### Is there a function that is its own derivative?

The derivative of an exponential function is a constant times itself. Using this definition, we see that the function has the following truly remarkable property. Hence is its own derivative. In other words, the slope of the plot of is the same as its height, or the same as its second coordinate.

### How do you integrate an ex?

0:044:09(5 of 5) Integrating the form "e to the x power" - YouTubeYouTube

### What is the derivative for e x 2?

We know how to differentiate x2 (the answer is 2x)...Using the chain rule to find the derivative of e^x^2.
ex2► Derivative of ex2 = 2xex2
e^(x^2)► Derivative of e^(x^2) = 2xex2
e x 2► Derivative of e x 2 = 2xex2
e to the x squared► Derivative of e to the x squared = 2xex2

### What is the derivative of y e 2x?

Answer: On differentiation we get dy / dx = 2e2x . Let us see how we will use the concept of differentiation to find the value of derivative dy / dx. Explanation: The function that is given to us is y = e2x.

### Why is the exponential's derivative its own derivative?

Therefore, the exponential is its own derivative because it is the solution to the ODE y'=y. You've got to respect the answer of someone with Euler in his/her username. Let's work backwards, start off with the question of what a function that is it's own derivative looks like.

### Why is the derivative of e 2x the same as E ^ X?

e is a special case because this quirk exists long its entire curve. Also, don't forget that the derivative of e 2x is 2e 2x - only e x acts as a derivation identity. only e x acts as a derivation identity. The class of functions of the form Ce x , rather. Thanks, that make sense now. Good explaination

### Why is the derivative of a power series always the same?

The curious thing about it is that each term is the derivative of the next term in the series, so as the series is infinite, taking the derivative basically keeps everything the same. Why that power series works is a whole different kettle of fish, though. This is exactly what it means for growth to be exponential.

### When do you change the derivative of logax?

The derivative of logax. According to the rule for changing from base e to a different base a: Topic 20 of Precalculus. a) when x is greater than 1 and becomes larger. That derivative approaches 0, that is, becomes smaller. b) when x is less than 1 and becomes smaller.