# How do you differentiate f(x)=sqrt(3+x^2)  using the chain rule?

Oct 27, 2015

You can do it like this:

#### Explanation:

$f \left(x\right) = \sqrt{3 + {x}^{2}}$

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

$\therefore f ' \left(x\right) = \frac{1}{2} {\left(3 + {x}^{2}\right)}^{- \frac{1}{2}} \times 2 x$

$\therefore f ' \left(x\right) = \frac{\cancel{2} x}{\cancel{2} \sqrt{3 + {x}^{2}}}$

$\therefore f ' \left(x\right) = \frac{x}{\sqrt{3 + {x}^{2}}}$