Question

derivative of y=-cos^-1(1/x^3)

Answer 1

d/dx(-cos^(-1)(1/x^3)) = -3/(sqrt(1-1/x^6) x^4)

Answer 2

\[y=-\cos^{-1}\left(\frac{1}{x^3}\right)\\
\cos (-y)=\frac{1}{x^3}\\
\cos y=\frac{1}{x^3}\]
Implicit differentiation yields
\[-\sin y~\frac{dy}{dx}=-\frac{3}{x^4}\\
\frac{dy}{dx}=\frac{3}{x^4}\csc y\]