For the function

$y=x^{2}$

$\Delta x=0.1$

$x=10$

$\frac{d y}{d x}=2 x$

$\Rightarrow\left(\frac{d y}{d x}\right)_{x=10}=20$

$\Rightarrow \Delta y=d y=\frac{d y}{d x} d x=20 \times 0.1=2$