Find $\frac{dy}{dx}$ if $y=\frac{\sqrt[\phantom{2}]{x}-1}{x^{3}1}$

a$)\frac{5x^{3}6\sqrt[\phantom{2}]{x^3}1}{2\sqrt[\phantom{2}]{x}(x^{3}1{)}^2}$

b$)\frac{-5x^3-6\sqrt[\phantom{2}]{x^3}1}{2\sqrt[\phantom{2}]{x}(x^{2}1{)}^2}$

c$)\frac{5x^3-6\sqrt[\phantom{2}]{x^3}1}{2\sqrt[\phantom{2}]{x}(x^{3}1{)}^2}$

d$)\frac{-5x^{3}6\sqrt[\phantom{2}]{x^5}-1}{2\sqrt[\phantom{2}]{x}(x^{3}1{)}^2}$

e$)\frac{-5x^{3}6\sqrt[\phantom{2}]{x^3}1}{2\sqrt[\phantom{2}]{x}(x^{2}1{)}^2}$

Find $\frac{dy}{dx}$ if $y=(x^3-2)\sqrt[3]{(3x^2-5)}$

a$.3x^2\sqrt[3]{3x^2-5}\frac{2x(x^3-2)}{\sqrt[8]{(3x^2-5{)}^2}}$

b$.3x^2\sqrt[3]{3x^2-5}\frac{2x^2(x^3-2)}{\sqrt[\phantom{2}]{(3x^2-5{)}^2}}$

c$.3x^2\sqrt[3]{3x^2-5}\frac{2x(x^3-2)}{\sqrt[V]{(3x^3-5)}}$

d$.\frac{z^2(11x^3-15x-4)}{8(3x^2-5{)}^2}$

e$.\frac{x(11x^3-15x-4)}{\sqrt[\phantom{2}]{(3x^2-5{)}^2}}$

Note: There are TWO correct answers for #$2.$

$3.$ Find the equation of tangent to the graph of $y=10-3x-x^2$ at the point where the curve intersects the right hand side of $x-$axis $.$

a$)y=-7x14$

b$)y=7x10$

c$)y=-7x-14$

d$)y=7x-14$

e$)y=-7x-10$

$4.$ Find $f^{(3)}(x)$ if $f(x)=3x^4-4x^{3}5x^{2}2x-\frac{4}{x}$

a$)72-\frac{24}{5}$

b$)72x^2-24\frac{24}{x^4}$

c$)72x^2-24x\frac{2}{x}$

d$)72x-\frac{24}{x}$

e$)72x-24\frac{24}{x}$