Recommended to be used when the Inverse function theorem is being employed in a question, and also for those users that need help understanding it.

For functions of a single variable, the theorem states that if $f$ is a continuously differentiable function with a non-zero derivative at the point $a$, then $f$ is invertible in a neighbourhood of $a$, the inverse is continuously differentiable, and $(f^{-1})^{\prime}(f(a))=\cfrac{1}{f^{\prime}(a)}$