Chapter 3: Derivatives - Section 3.5 - Derivatives of Trigonometric Functions - Exercises 3.5 - Page 141: 6

The Derivative is: $y'=-x^2\csc^2 x+2x\cot x+\frac{2}{x^3}$

$y=x^2\cot x-\frac{1}{x^2}$ Applying Derivative Rules: $y'=f'(x)+g'(x)$ and $f'(x)=h'(x)\cdot r(x)+h(x)\cdot r'(x)$ $y'=[((2)x^{2-1})(\cot x)+(x^2)(-\csc^2 x)] - (-2)x^{-2-1}$ $y'=2x\cot x-x^2\csc^2 x+\frac{2}{x^3}$ $y'=-x^2\csc^2 x+2x\cot x+\frac{2}{x^3}$