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Find step-by-step Discrete math solutions and your answer to the following textbook question: Let n be a positive integer. What is the nth derivative of x^n ...

Nth Derivative of x^(n-1) ; dn[xn−1]dxn=0,∀n∈N∗ ; f(x)=xn−1 ; f′(x)=(n−1)xn−2 ; f″(x)=(n−2)(n−1)xn−3 ; fn(x)=?

edit: I was also able to complete the proof above using the general leibniz rule for nth derivative of products, but still it seems like I'm ...

27.01.2017 · f '''(x) = n(n −1)(n − 2)xn−3. and so on until n −k = 0 where k is the order of the derivative. When we finish, we get: f (k)(x) = n(n −1)(n − 2)⋯(n − k + 1)xn−k. When we go all the way to n = k, then: f (n)(x) = n(n −1)(n − 2)⋯(1)x01. which is a constant equaling n!, as n! = n(n − 1)(n −2)⋯(2)(1), and x0 = 1 which ...

We use the General Leibniz rule - Wikipedia : Differentiating is easy. The -th derivative of (where ) is . So. I can't see how to make this any simpler so ...

Corollary to Nth Derivative of Mth Power. Let n∈Z be an integer such that n≥0. The nth derivative of xn with respect to x is: dndxnxn=n!

Examples: Finding The nth Derivative · f′(x) = nx · f′′(x) = n(n – 1)x · f′′′(x) = n(n – 1) (n – 2)x ...

nth Derivative. Taking the derivatives of the function n number of times is known as nth derivative of the function. A general formula for all of the successive derivatives exists. This formula is called the nth derivative, f' n (x). It can be denoted as:

n! Explanation: f(x)=xn f'(x)=nxn−1 ' f''(x)=n(n−1)xn−2 ... f(n)(x)=n(n−1)...3.2.1x0 =n! Or by induction on n if you want a formal proof.

If y = xn-1 ln x, then the nth order derivative of y with respect to x at x = 1 2 is: This question was previously asked in. Junior Executive (ATC) Official ...

23.06.2017 · in this video i will show you how to find the nth derivative of x^n step by step please subscribe to my channel to support me https://www.youtube.com/channel...

The nth derivative refers to any one of a number of higher level derivatives of a function . When you take the derivative of function one time, you get the first derivative . Differentiating the new function another time gives you the second derivative .

How do you find the nth derivative of the function f(x)=xn? · Hint: In order to determine the nth order derivative, first find out some derivative of the given ...

19.10.2016 · 3 Answers3. Show activity on this post. The following is a proof by induction. The base case is k = 0, for which the function is x n. Suppose that we are given that d m d x m ( x n) = n! ( n − m)! x n − m. Then, Hence, the induction is complete. Now, put k = n, and you get d n d x n ( x n) = n!, which is a constant.