You can use a shortcut to determine a higher-order derivative of a sine function by recognizing the cyclic pattern that repeats every four derivatives. To use the shortcut, begin by dividing the order of the derivative by `4`. If the remainder is `0`, the derivative returns to the original function. If the remainder is `1`, the derivative progresses to the next function in cycle. If the remainder is `2`, the derivative is the negative of the original function. If the remainder is `3`, the derivative is the negative of the next function in the cycle.

`-6 cos(x)`