Problem $13$

Differentiate the following functions w$.$r$.$t$.x$ :

$($a$)\frac{3}{5}{x}^2-2x^7+\frac{1}{8}-\sqrt[\phantom{2}]{x}$

$($b$)(2x^2-1)(x^4-1)$

$($c$)(x^5+\frac{1}{x})(x^5+1)$

Problem $14$

Differentiate the following functions w$.$r$.$t$.x$ :

$($a$)\frac{1}{x^6}$

$($b$)x^{-1}(x^2+1)\sqrt[\phantom{2}]{x}$

$($c$)\frac{1}{\sqrt[\phantom{2}]{x^3}}$

$5$ of $6$

Problem $15$

Differentiate the following functions w$.$r$.$t$.x$ :

$($a$)\frac{\sqrt[\phantom{2}]{x}-2}{\sqrt[\phantom{2}]{x}+1}$

$($b$)\frac{x^2-1}{x^2+1}$

$($c$)\frac{x^2+x+1}{x^2-x+1}$

Problem $16$

Compute the following limits:

$($a$)\underset{x2}{lim}(x^2+3x-5)$

$($b$)\underset{y-3}{lim}\frac{1}{y+8}$

$($c$)\underset{x0}{lim}\frac{x^3-2x-1}{x^5-x^2-1}$

$($d$)\underset{x0}{lim}\frac{x^3+3x^2-2x}{x}$

$($e$)\underset{h0}{lim}\frac{(x+h{)}^3-x^3}{h}$