Find the real numbers $a,b$ and $c$ if the parabola $y=a{x}^{2}bxc$ passing $(1,1)$ and the tangent line at the point $(2,1)$ is perpendicular to the line $x2y-1=0.$

Find the derivative of the following functions.

vii$)y=(x\sqrt[\phantom{2}]{x}{)}^{50}$

x$)y=(2x^3-x{)}^8\sqrt[4]{x^{2}5x}$