Learn how we define the derivative using limits. Learn about a bunch of very useful rules (like the power, product, and quotient rules) that help us find derivatives quickly.

Let's explore how to find the derivative of any polynomial using the power rule and additional properties. The derivative of a constant is always 0, and we can pull out a scalar constant …

Learn differential calculus—limits, continuity, derivatives, and derivative applications.

The derivative of a function describes the function's instantaneous rate of change at a certain point - it gives us the slope of the line tangent to the function's graph at that point.

Let's explore a problem involving two functions, f and g, and their derivatives at specific points. Our goal is to find the derivative of a new function, h (x), which is a combination of these …

The following table lists the value of functions g and h , and of their derivatives, g ′ and h ′ , for x = 3 . ... Let function G be defined as G (x) = 2 g (x) h (x) + 8 .

What are the basic differentiation rules? ... The Sum rule says the derivative of a sum of functions is the sum of their derivatives. The Difference rule says the derivative of a difference of …

The dy/dx notation is useful because it emphasizes the idea that the derivative is a small change in the output divided by a small change in the input. And f' (x) is useful because it shows that …

The big idea of differential calculus is the concept of the derivative, which essentially gives us the direction, or rate of change, of a function at any of its points. Learn all about derivatives and …

Review all the common derivative rules (including Power, Product, and Chain rules).