Final answer:
The term for taking the fourth derivative of a function in calculus is the 'Fourth Order Derivative'. It involves successively differentiating the original function three times to obtain the third derivative, and then once more to acquire the fourth derivative. D) Fourth Order Derivative
Step-by-step explanation:
The question asks for the term used to describe the operation of taking the fourth derivative of a function. This is a concept from calculus, a branch of mathematics concerned with the properties and applications of derivatives.
In calculus, the process of finding the derivative of a function can be repeated multiple times. This is known as taking higher derivatives or higher-order derivatives.
The first derivative typically represents the rate of change, such as velocity being the first derivative of position with respect to time. The second derivative often represents the rate of change of the rate of change, such as acceleration being the second derivative of position. The terminology continues for successive derivatives.
The proper term for finding the fourth derivative of a function is the Fourth Order Derivative (option D).
To derive a fourth order derivative, one would start with the original function and take its first derivative. The process involves calculating the rate of change at each stage. After finding the first derivative, you would then find the second derivative, which is the derivative of the first derivative. Next, you calculate the third derivative, which is the derivative of the second derivative. Finally, the fourth derivative is the derivative of the third derivative.
An example is given with the function F = 2mk²x²; to find the acceleration a, one would first take the derivative of the velocity function. This scenario represents a physical application of the concept of differentiation in physics.