Q$1)$ if $y=log|)x$

Show that $\frac{dy}{dx}{|}_x|=+e$~~$-1\mathrm{.}04834$

Q$2)$ find $($:$\frac{d}{dx}(lo{g}_{(x+1)}(x+2){)}^x+x^x\}$

Q$3)$ find $\frac{d}{dx}(x^{x^{x^{-}}}+x\sqrt[\phantom{2}]{sinx+\sqrt[\phantom{2}]{sinx+\sqrt[\phantom{2}]{sinx+\sqrt[\phantom{2}]{sinx+\text{c}\text{d}\text{o}\text{t}\text{s}}}}})$

Q$4)$let $f(x)=a{x}^3+b{x}^2+cx+1,$ given that

$\underset{t1}{lim}\frac{f(t)-f(1)}{3t-3}=\frac{-f^{\text{'}\text{'}}(-1)}{2}=f^{\text{'}\text{'}}(2)=1.$ Show that

$g^{\text{'}\text{'}}(1)=2(ln2+1{)}^2+3(ln3+1{)}^2-1$

Where $g(x)=(((6a+1)x{)}^x+(c+b{)}^{(x^x)})$

Q$5)$ let $f(x)=ta{n}^{-1}(e^{ax}+b),$ find the values of a and b such that

$f^{\text{'}}(0)=2\mathrm{.}5$

$f^{\text{'}\text{'}}(0)=-10\mathrm{.}5$