The derivative of cos(x) is -sin(x) . This means that the rate of change of the cosine function at any point is equal to the negative of the sine function at that point. The derivative of cos(x) can be derived using the definition of limits, quotient rule, or Eulers complex representation of trigonometric functions. The derivative of all trigonometric functions can be calculated using the derivative of cos(x) and the derivative of sin(x) .