اگر ${f}'(x)=\frac{۱}{x+۱}$، $g(x)=\sqrt{x-۲}$ و $(fog)'(a)=\frac{۱}{۴}$، مقدار $a$ چقدر است؟
$y=fog(x)\Rightarrow {y}'={g}'(x){f}'(g(x))\Rightarrow {y}'(a)={g}'(a){f}'(g(a))$ ${y}'(a)=\frac{1}{2\sqrt{a-2}}\times \frac{1}{\sqrt{a-2}+1}=\frac{1}{4}\xrightarrow{\sqrt{a-2}=t}\frac{1}{t(t+1)}=\frac{1}{2}$ $\Rightarrow {{t}^{2}}+t-2=0\Rightarrow t=-2,1\xrightarrow{t \gt 0}\sqrt{a-2}=1\Rightarrow a=3$