Prove that if y = cotx then dy/dx = - (cscx)^2. Hint: cotx = cosx/sinx

Answer 1

y = cotx
y = cosx/sinx
dy/dx = (sinx(-sinx) - cosx(cosx) )/sin^2 x
this assumes you know how to take derivatives of sinx and cosx

= -(sin^2 x + cos^2 x)/sin^2 x
= -1/sin^2 x
= -csc^2 x or - (cscx)^2