# How do you differentiate y=sqrt(4x +3)?

Nov 2, 2016

 y = 2/(sqrt(4x+3)

#### Explanation:

Using chain rule, we first find the derivative of the form

$\frac{d}{\mathrm{dx}} \left(\sqrt{x}\right) = \frac{1}{2 \sqrt{x}}$

hence, we have,

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{2 \sqrt{4 x + 3}}$

But, we are not done yet. as we have a term containing x in it inside the square root.
Therefore, we differentiate the linear term inside the square root,

$\frac{d}{\mathrm{dx}} \left(4 x + 3\right) = 4$

Hence our answer is 4/(2sqrt(4x+3)) = 2/(sqrt(4x+3)