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

Jan 14, 2016

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

#### Explanation:

We may use the following rules in conjunction :

$\frac{d}{\mathrm{dx}} \tan \left[u \left(x\right)\right] = {\sec}^{2} u \cdot \frac{\mathrm{du}}{\mathrm{dx}}$

$\frac{d}{\mathrm{dx}} {\left[u \left(x\right)\right]}^{n} = n {\left[u \left(x\right)\right]}^{n - 1} \cdot \frac{\mathrm{du}}{\mathrm{dx}}$

Hence we obtain :

$f ' \left(x\right) = {\sec}^{2} \left(\sqrt{{x}^{2} - 3}\right) \cdot \frac{1}{2} {\left({x}^{2} - 3\right)}^{- \frac{1}{2}} \cdot \left(2 x\right)$