# How do you differentiate f(x)=-sinsqrt(1/(x^2)) using the chain rule?

Nov 1, 2016

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