$\lim_{x\rightarrow 0} \frac{\sqrt{1+x}-\sqrt{1-x}}{x} * \frac{\sqrt{1+x}+\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}$ multiplying numerator and denominator by $\frac{\sqrt{1+x}+\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}$
$\lim_{x\rightarrow 0} \frac{(1+x)-(1-x)}{x*\sqrt{1+x}+\sqrt{1-x}}$
After subtracting and dividing we get
$\lim_{x\rightarrow 0} \frac{2}{1*\sqrt{1+x}+\sqrt{1-x}}$
Applying limits we get
$\frac{2}{\sqrt{1}+\sqrt{1}} = \frac{2}{2} = 1$
Hence answer is option c