Differential calculus is the study of the slopes of functions and their application to real world problems. The slope of a function $f(x)$ at a specific point is called a derivative and is denoted by two common notations: $f'(x)$ and $\frac{df}{dx}$. We provide a listing of real world examples where derivatives are used to describe real world phenomenon.
The Chain Rule shows how to find the derivative of a function composition. The Chain Rule states that $\frac{d}{dx}\left[f\circ g\right] =\frac{df}{dg}\cdot\frac{dg}{dx}.$
We present here the most important differentiation formulas. We include derivatives of $x^n$, the product rule, the quotient rule, and the chain rule.
The Leibniz notation is where we denote a function's derivative by $\frac{df}{dx}$. We provide an explanation of where the Leibniz notation comes from.
We motivate the fact that we can find as many other derivatives of a function as possible and emphasize the use of the Leibniz notation to describe them. We calculate all of the derivatives of $f(x)=x^2$ and $f(x)=e^x$. We provide links to lessons that detail the meaning of the second derivative.
An antiderivative of the function $f(x)$ is another function $F(x)$ where $F\,'(x)=f(x)$.