Contents of Derivatives

Evaluate the following derivatives:

For g(x) = 24x³ +3x² + 7x + 1,

Evaluate the following derivatives

D_x $\left(\vphantom{ \dfrac{x}{x^{2}-2}}\right.$ ${\dfrac{{x}}{{x^{2}-2}}}$ $\left.\vphantom{ \dfrac{x}{x^{2}-2}}\right)$
D_x $\left(\vphantom{ x\sqrt{1-x^{2}}}\right.$ x $\sqrt{{1-x^{2}}}$ $\left.\vphantom{ x\sqrt{1-x^{2}}}\right)$
${\dfrac{{d^{2}}}{{dx}}}$ $\left(\vphantom{ \dfrac{\cos ^{2}x}{1+\tan x}}\right.$ ${\dfrac{{\cos ^{2}x}}{{1+\tan x}}}$ $\left.\vphantom{ \dfrac{\cos ^{2}x}{1+\tan x}}\right)$
${\dfrac{{d}}{{dx}}}$ $\sqrt[4]{{\dfrac{x^{2}+x+1}{x^{2}-x+1}}}$