Unlike a straight line, a curve's slope constantly changes as you move along the graph. Calculus introduces students to the idea that each point on this graph could be described with a slope, or an "instantaneous rate of change." The tangent line is a straight line with that slope, passing through that exact point on the graph. To find the equation for the tangent, you'll need to know

When integrating functions involving polynomials in the denominator, partial fractions can be used to simplify integration. New students of calculus will find it handy to learn how to decompose functions into partial fractions not just for integration, but for more advanced studies as well.

The Gaussian function f(x)=e−x2{\displaystyle f(x)=e^{-x^{2}}} is one of the most important functions in mathematics and the sciences. Its characteristic bell-shaped graph comes up everywhere from the normal distribution in statistics to position wave packets of a particle in quantum mechanics. Integrating this function over all of x{\displaystyle x} is an extremely common task, but it

Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of mathematics, and underpins many of the equations that describe physics and mechanics. You will probably need a college level class to understand calculus well, but this article can get you started and help you watch for the important

In calculus, when you have an equation for y written in terms of x (like y = x -3x), it's easy to use basic differentiation techniques (known by mathematicians as "explicit differentiation" techniques) to find the derivative. However, for equations that are difficult to rearrange with y by itself on one side of the equals sign (like x + y - 5x + 8y + 2xy = 19), a different approach is

The derivative is an operator that finds the instantaneous rate of change of a quantity, usually a slope. Derivatives can be used to obtain useful characteristics about a function, such as its extrema and roots. Finding the derivative from its definition can be tedious, but there are many techniques to bypass that and find derivatives more easily.

Integration by parts is a technique used to evaluate integrals where the integrand is a product of two functions. ∫f(x)g(x)dx{\displaystyle \int f(x)g(x)\mathrm {d} x} Integrals that would otherwise be difficult to solve can be put into a simpler form using this method of integration.

This is intended as a guide to assist those who must occasionally calculate derivatives in generally non-mathematical courses such as economics, and can also be used as a guide for those just starting to learn calculus. This guide is meant for those who are already comfortable with algebra. Note: The symbol for a derivative used in this guide is the ' symbol, * is used for

Calculus is one of the most important tools used in a variety of sciences, engineering, computers and physics. But it has many other, simpler applications to everyday life as well. Anyone, no matter how mathematically inclined, can gain a basic understanding of calculus and find enjoyment in it. There is much more to it than just cranking out numbers and finding solutions to problems.

It is commonly said that differentiation is a science while integration is an art. The reason is because integration is simply a harder task to do—while a derivative is only concerned with the behavior of a function at a point, an integral, being a glorified sum, integration requires global knowledge of the function. So while there are some functions whose integrals can be evaluated