The derivative of root 3x is equal to √3/(2√x). In this post, we will learn how to find the derivative of the square root of 3x.

## Derivative of root 3x by Power Rule

Let us find the derivative of square root of 3x by the power rule of derivatives. The rule says that the derivative of x^{n} is given by the formula:

$\frac{d}{dx}$(x^{n}) = nx^{n-1}.

Now, $\dfrac{d}{dx}(\sqrt{3x})$

= √3 × $\dfrac{d}{dx}(\sqrt{x})$

= √3 × $\dfrac{d}{dx}(x^{1/2})$ as we know that square root of x is written as x to the 1/2.

= $\sqrt{3} \times \dfrac{1}{2}x^{1/2 -1}$ by the above power rule.

= $\dfrac{\sqrt{3}}{2}x^{-1/2}$

= $\dfrac{\sqrt{3}}{2\sqrt{x}}$.

So the derivative of square root 3x is √3/(2√x), and this is obtained by using the power rule of derivatives.

Next, we find the derivative of root 3x by the chain rule of derivatives.

## Derivative of root 3x by Chain Rule

Let z=3x.

So dz/dx =3.

By the chain rule, the derivative of root 3x will be equal to

$\dfrac{d}{dx}(\sqrt{3x})$

= $\dfrac{d}{dz}(\sqrt{z})$ × $\dfrac{dz}{dx}$

= $\dfrac{1}{2\sqrt{z}}$ × $\dfrac{dz}{dx}$ as the derivative of root x is 1/(2√x).

= $\dfrac{1}{2\sqrt{3x}}$ × 3 as z=3x.

= √3/(2√x)

So the derivative of square root 3x by chain rule is √3/(2√x).

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## FAQs

### Q1: What is the derivative of square root of 3x?

Answer: The derivative of the square root of 3x is √3/(2√x).