# How do you differentiate f(x) = sin ( x² ln(x) )?

$\frac{\mathrm{df} \left(x\right)}{\mathrm{dx}} = x \left(2 \ln x + 1\right) \cos \left({x}^{2} \ln x\right)$
$\frac{\mathrm{df} \left(x\right)}{\mathrm{dx}} = \frac{d}{\mathrm{dx}} \left(\sin \left({x}^{2} \ln x\right)\right) = \cos \left({x}^{2} \ln x\right) \cdot \left(2 x \ln x + {x}^{2} \frac{1}{x}\right)$
$\frac{\mathrm{df} \left(x\right)}{\mathrm{dx}} = x \left(2 \ln x + 1\right) \cos \left({x}^{2} \ln x\right)$