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

$\frac{\sin \ln {x}^{3} + 3 \cos \ln {x}^{3}}{2 \sqrt{x \sin \ln {x}^{3}}}$
$f ' \left(x\right) = \frac{1}{2 \sqrt{x \sin \ln {x}^{3}}} \cdot \left(1 \cdot \sin \ln {x}^{3} + \cancel{x} \cdot \cos \ln {x}^{3} \cdot \frac{1}{\cancel{{x}^{3}}} \cdot 3 \cancel{{x}^{2}}\right)$
$= \frac{\sin \ln {x}^{3} + 3 \cos \ln {x}^{3}}{2 \sqrt{x \sin \ln {x}^{3}}}$