Basics of calculus and how to differentiate and integrate

Calculus is a branch of mathematics that deals with rates of change and the accumulation of quantities. In this tutorial, we will cover the basics of calculus, including the concepts of differentiation and integration. Differentiation is a fundamental concept in calculus that involves finding the rate of change, or derivative, of a function at a given point. The derivative of a function tells us how the value of the function is changing with respect to its input. For example, if we have a function that describes the position of an object over time, the derivative of the function would tell us the object's speed at a given time. To find the derivative of a function, we use a process called differentiation. Differentiation involves taking the limit of the difference quotient, which is a measure of the change in the function over a small interval. The difference quotient is calculated by dividing the difference in the function's output by the difference in its input. Integration is the inverse of differentiation, and it involves finding the area under a curve or the accumulation of a quantity over a given interval. The process of integration involves using techniques such as substitution and integration by parts to rewrite the integral in a form that can be evaluated. In this tutorial, we will go over these concepts in more detail and practice finding the derivatives and integrals of various functions. By the end of this tutorial, you should have a good understanding of the basics of calculus and be able to apply differentiation and integration to solve problems involving rates of change and accumulation of quantities.