# How do you find the derivative of y =sqrt(3x+1)?

Jul 31, 2014

When you're differentiating radicals, the key is to rewrite them in rational exponent form:

$y = {\left(3 x + 1\right)}^{\frac{1}{2}}$

Now it's more clear that we can apply the power rule and then the chain rule to find this function's derivative:

$\frac{\mathrm{dy}}{\mathrm{dx}} = 3 \cdot \left(\frac{1}{2} \cdot {\left(3 x + 1\right)}^{- \frac{1}{2}}\right)$

And now all we need to do is simplify a bit:

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