Differentiation and integration are fundamental concepts in calculus that help us solve a wide range of mathematical problems. Let's break down these concepts step-by-step to gain a deeper understanding.

Differentiation is the process of finding the rate at which a function is changing. It allows us to calculate the slope of a curve at any given point. To differentiate a function, we use the power rule, which states that the derivative of a constant multiplied by a variable raised to a power is the constant multiplied by the power of the variable reduced by one. For example, if we have the function f(x) = 3x^2, the derivative of f(x) would be f'(x) = 6x.

Integration is the reverse process of differentiation. It helps us find the area under a curve or the accumulated change over a certain interval. To integrate a function, we use the power rule in reverse. For example, if we want to integrate f'(x) = 6x, we would get f(x) = 3x^2 + C, where C is the constant of integration.

In summary, differentiation enables us to find the rate of change or slope of a function, while integration allows us to find the area under a curve or the accumulated change. These concepts are crucial in various fields of study, including physics, engineering, and economics.