Show that the function

we have,

$f(x)=10^{x}$

$\therefore f^{\prime}(x)=10^{x} \log 10$

Now,

$X \in R$

$\Rightarrow 10^{x}>0$

$\Rightarrow 10^{x} \log 10>0$

$\Rightarrow f^{\prime}(x)>0$

Hence, $f(x)$ in an increasing function for all $x$