Question

find the derivative of csc exponent of -1 3x?

Answer 1

\[y = \csc ^{-1}(3x)\]
\[\csc y = 3x\]
\[\sin y = \frac{1}{3x}\]
now differentiate both sides
\[y' \cos y = -\frac{1}{3x^{2}}\]
\[y' = -\frac{\sec y}{3x^{2}}\]