\frac{\cos  x^2}{\sqrt{ \sin  x^2}} \lim_{h\to 0+} \, \frac{\sin \left(\frac{h^2}{2}+h x\right)}{h}=\frac{\cos  x^2}{\sqrt{ \sin  x^2}} \lim_{h\to 0+} \, \frac{\sin \left(\frac{h^2}{2}+h x\right)}{\frac{h^2}{2}+h x} \frac{\left(\frac{h^2}{2}+h x\right)}{h}=\frac{\cos  x^2}{\sqrt{ \sin  x^2}} \lim_{h\to 0+} \, \frac{\sin \left(\frac{h^2}{2}+h x\right)}{\frac{h^2}{2}+h x}\lim_{h\to 0+}  \frac{\left(\frac{h^2}{2}+h x\right)}{h}=\frac{\cos  x^2}{\sqrt{ \sin  x^2}}*1*\lim_{h\to 0+}  \left(\frac{h}{2}+x\right)=\frac{x \cos x^2}{\sqrt{ \sin  x^2}}