# What is the differentiation of ln Sinx?

## What is the differentiation of ln Sinx?

ln is nothing but natural logarithm so ‘ln’ has to be treated as logarithm function. First consider the given function is in the form of ln(x) and first derivative then the internal derivative of sinx has to applied and at last internal derivative of ‘x’ which is equal to 1. = cosx/sinx = cotx .

How do you find the absolute value of Sinx?

You say that y = | sin x |, so the y-values can only be 0 or positive. If you take the graph of f(x) = sin x (without the absolute value), reflect all of the graph that is below the x-axis, across the x-axis, you will get the graph of y = | sin x |. That’s what the absolute value does.

### Is ln absolute value?

Yes. Assuming that you mean by \ln|x| a function that is defined both for positive x and for negative x, that means that the derivative must be \frac {1}{|x|}, which is also defined both for positive and negative x. You can only leave out the absolute value signs if you limit your domain to positive x.

What is the value of ln 1?

0
log 1 = 0 means that the logarithm of 1 is always zero, no matter what the base of the logarithm is. This is because any number raised to 0 equals 1. Therefore, ln 1 = 0 also.

#### What is the period of absolute value Sinx?

The period of the sine function is ​2π​, which means that the value of the function is the same every 2π units.

What is the period for Y Sinx?

Period and Amplitude of Basic Trig Functions

A B
Period of y=sin x
Period of y=cos x
Period of y=tan x π
Period of y=cot x π

## What is the domain of LN Sinx?

As we know that ln x is defined on (0, ∞), so the domain for the function ln(sin x) is the set of x so that sin x is positive. In the case of one period, say, from 0 to 2π, the domain is (0,π).

How to find the derivative of absolute value of SiNx?

In this section, we will learn, how to find the derivative of absolute value of (sinx). Let |f (x)| be the absolute-value function. Then the formula to find the derivative of |f (x)| is given below. Based on the formula given, let us find the derivative of absolute value of sinx.

### What is the derivative of ln ( SiNx )?

d dx (ln(sin(x))) = 1 sin(x) ⋅ cos(x) = cos(x) sin(x) = cot(x)

Are there any negative numbers in ln ( x )?

That is, negative numbers are not in the domain of a logarithmic function. However, in ln(|x|), negative numbers are made positive. For example, both e2 and −e2, when plugged into ln(|x|), result in ln(e2) = 2.

#### How do you graph Ln ( abs ( x ) )?

For example, both e2 and −e2, when plugged into ln(|x|), result in ln(e2) = 2. In effect, adding the absolute value makes both the positive and negative realms available for the natural logarithm, in effect reflecting the graph over the y -axis, while retaining itself on the positive side: