The derivative of cos(4x) is -4*sin(4x)while the general derivative form of cos(y) is -dy*sin(y). Since there is a variable contained in the bracket, the derivative of it must also be taken due to the chain rule. Since the derivative of 4x is simply 4, a constant of 4 is placed in front of and multiplied by the -sin(4x) term.
The derivative of an equation is equal to the instantaneous slope at a specific point. A derivative can be estimated by plotting an equation and using nearby points to create a slope estimate. A precise derivative must be calculated using formulas for different forms of equations.