Find the derivative of x^2 cotx - 1/x^2

Question

Should I use the product rule first and then the subtraction rule? Thank you for your help

Answer 1

Remeber the product rule in derivatives is d/dx(uv) = uv'+vu'

Given function is x^2Cotx-1/x^2

Aplly derivative with respect of x.

d/dx(x^2Cotx-1/x^2)

= d/dx(x^2Cotx)-d/dx(1/x^2)

= x^2(-Csc^2x)+Cotx(2x)-(-2/x^3)

= -x^2Csc^2x+2xCotx+2/x^3