## What is the derivative of ln square root X?

1 / x

To use the chain rule, we’re going to have to find f ‘ (g(x)), and g ‘ (x). Both of these derivatives are well-known. The derivative of ln(x) is 1 / x. The derivative of √x is (1/2)x(-1/2), or 1/(2√x).

## What is the derivative of square root X?

12√x

The derivative of √x is 12√x . Remember that we can rewrite surds like this in index notation. For this case, √x=x12 .

**What is the derivative of ln squared?**

0

The derivative of y=ln(2) is 0 . Remember that one of the properties of derivatives is that the derivative of a constant is always 0 .

**What is the derivative of ln 5x?**

But ln(5) is a constant, so its derivative is 0 .

### What does Lnx 2 mean?

ln2x is simply another way of writing (lnx)2 and so they are equivalent. However, these should not be confused with lnx2 which is equal to 2lnx. There is only one condition where ln2x=lnx2 set out below. ln2x=lnx2→(lnx)2=2lnx. ∴lnx⋅lnx=2lnx.

### How do you take the derivative of ln?

The derivative of the natural logarithmic function (ln[x]) is simply 1 divided by x. This derivative can be found using both the definition of the derivative and a calculator….Derivatives Of Logarithmic Functions

- y = ln(x2 x)
- y = (log7 x) 1/3
- y = ln(x4˙sin x)
- y = lnx/[1 + ln(2x)]

**What is the derivative of ln (5x)?**

A student comfortable with the natural logarithm function and its properties might think of this: One could reason as follows: y=ln(5x)=ln(5)+ln(x). But ln(5) is a constant, so its derivative is 0.

**What is the derivative of ln(x)?**

The derivative of ln (x) is 1 x. In certain situations, you can apply the laws of logarithms to the function first, and then take the derivative.

#### What is the derivative of ln(2x)?

f (g (x)) = ln (2x) ⇒ f’ (g (x)) = 1/2x. (The derivative of ln (2x) with respect to 2x is (1/2x)) = 1/x . Using the chain rule, we find that the derivative of ln (2x) is 1/x. Finally, just a note on syntax and notation: ln (2x) is sometimes written in the forms below (with the derivative as per the calculations above).

#### How do you calculate derivative?

The first step to finding the derivative is to take any exponent in the function and bring it down, multiplying it times the coefficient. We bring the 2 down from the top and multiply it by the 2 in front of the x. Then, we reduce the exponent by 1. The final derivative of that term is 2*(2)x1, or 4x.