Final answer:
The mathematical operation you perform to find the derivative of a given function is differentiation.
Step-by-step explanation:
The mathematical operation you perform to find the derivative of a given function is differentiation. Differentiation is a fundamental concept in calculus that involves finding the rate at which a function changes at any given point. It allows us to determine the slope of a curve or the instantaneous rate of change.
To find the derivative of a function, you apply the rules of differentiation, such as the power rule, product rule, and chain rule. These rules guide you step-by-step in finding the derivative of various functions.
For example, if you have the function f(x) = 2x^3 - 5x^2 + 3x, you can find its derivative by differentiating each term separately. Applying the power rule, the derivative of 2x^3 is 6x^2, the derivative of -5x^2 is -10x, and the derivative of 3x is 3. Simplifying these derivatives yields the derivative f'(x) = 6x^2 - 10x + 3.