Differentiate the following logarithmic functions.

a$.\text{'}$F$\text{'}$Open paren. $\text{'}$X$\text{'}$ Close paren. equals lnOpen paren. $\text{'}$X$\text{'}$ raised to the $2\mathrm{.}00$ power; Close paren.f$($x$)=$ln$($x$2\mathrm{.}00)$f$\backslash$mleft$($x$\backslash$mright$)=\backslash$ln $\backslash$mleft$($x$^\{2\mathrm{.}00\}\backslash$mright$)$

b$.\text{'}$F$\text{'}$Open paren. $\text{'}$X$\text{'}$ Close paren. equals $1\mathrm{.}05\text{'}$X$\text{'}$ squared centered dot lnOpen paren. $\text{'}$X$\text{'}$ Close paren.f$($x$)=1\mathrm{.}05$x$2$ln$($x$)$f$\backslash$mleft$($x$\backslash$mright$)=1\mathrm{.}05$x$^2\backslash$cdot $\backslash$ln $\backslash$mleft$($x$\backslash$mright$)$

c$.\text{'}$F$\text{'}$Open paren. $\text{'}$X$\text{'}$ Close paren. equals open square bracket lnOpen paren. $\text{'}$X$\text{'}$ Close paren. plus $\text{'}$X$\text{'}$ close square bracket to the Open paren. one quarter Close paren. ;f$($x$)=[$ln$($x$)+$x$](14)$f$\backslash$mleft$($x$\backslash$mright$)=\backslash$left$\backslash$lbrack $\backslash$ln $\backslash$mleft$($x$\backslash$mright$)+$x$\backslash$right$\backslash$rbrack $^\{\backslash$left$(\backslash$frac$\{1\}\{4\}\backslash$right$)\}$