# What is the nth derivative of LNX?

## What is the nth derivative of LNX?

The nth derivative of ln(x) for n≥1 is: dndxnlnx=(n−1)!

## What is nth derivative test?

Applicable Course(s): 3.0 Calculus. The author describes nth derivative test, a generalization of 2nd derivative test, then applies it to give a quick proof of a condition for determining when the graph of a function and its Taylor polynomials intersect.

What is derivative of log 1x?

We know that the derivative of log |x| is 1/x. Hence, if we have to differentiate log(1 + x + x2), we use the chain rule. Therefore, derivative of log(1 + x + x2) = 1 / (1 + x + x2) .

### What is second derivative test used for?

The second derivative may be used to determine local extrema of a function under certain conditions. If a function has a critical point for which f′(x) = 0 and the second derivative is positive at this point, then f has a local minimum here.

### Which is the formula for the nth derivative of the function?

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: Let us see the following example.

Which is the higher order derivative of the function?

First, let us see what are the higher order derivatives of the function and how we can calculate them. If the derivative of a function, the first derivative, f’ (x), is differentiated, a new function is obtained called the second derivative, f” (x). If this function is differentiated again, a third derivative, f”’ (x), is obtained.

#### How to calculate the derivative of a function?

Calculate the 1st, 2nd, 3rd, 4th and 5th derivatives of the following function: Let us compute the first derivative of the above function first. To calculate the derivative of the above function, we will use multiple derivative rules which include sum and difference, power and constant rule.

#### How to compute the th derivative of Cos?

Compute the first four derivatives of Cos using the general formula. Copy to clipboard. Compute the billionth derivative of Cos with blinding speed. Copy to clipboard. Compute the th derivative of ArcTan. Copy to clipboard. Obtain elementary answers for specific values of .

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