Posts Tagged ‘derivative’
Friday, October 30th, 2009
How to Find Higher Order Derivatives
Description
A detailed tutorial on higher order derivatives. Step by step tutorial including several examples of higher order derivatives for reference.
Overview
A higher order derivative is a derivative with a power other than one – that is, a derivative is referred to as a first derivative, and the higher order derivatives are a second derivative, third derivative, etc. The second derivative is the derivative of the first derivative, and the third derivative is the derivative of the second derivative. When you know all the rules of taking derivatives, taking second and third derivatives are simple. Simply take the derivative and pretend it is another equation. When you go up beyond the third derivative this can get more challenging, as there will be many more parts to the equation.
Tags: antiderivative, Calculus, chain, derivative, First, higher, integral, order, power, product, quotient, rule, second, third
Posted in Calculus | No Comments »
Thursday, October 22nd, 2009
How to Identify a Concave Function
Description
A detailed tutorial on concave functions. Step by step tutorial including several examples of concave functions and concave down curves for reference.
Overview
When a function forms the graph of a curve, there are two types of functions it could be: a convex function, or a concave function. In this tutorial, we will discuss concave functions. A concave function is one with the endpoints facing down, forming the shape of an upside down bowl. When looking at the graph of a concave function, we say that it is concave down. Concavity can be found by the second derivative test in calculus.
Tags: Calculus, concave, concavity, convex, curve, derivative, down, endpoint, equation, function, graph, interval, second, test, up
Posted in Calculus | No Comments »
Thursday, October 22nd, 2009
How to Identify a Convex Function
Description
A detailed tutorial on convex functions. Step by step tutorial including several examples of convex functions and concave up curves for reference.
Overview
When a function forms the graph of a curve, there are two types of functions it could be: a convex function, or a concave function. In this tutorial, we will discuss convex functions. A convex function is one with the endpoints facing up, forming the shape of a bowl. When looking at the graph of a convex function, we say that it is concave up. Concavity can be found by the second derivative test in calculus.
Tags: Calculus, concave, concavity, convex, curve, derivative, down, endpoint, equation, function, graph, interval, second, test, up
Posted in Calculus | No Comments »
Friday, October 9th, 2009
Explanation of Leibniz Notation
Description
A detailed tutorial on Leibniz notation. Step by step tutorial including several examples of Leibniz notation for reference. Knowledge of Leibniz notation is mandatory for calculus.
Overview
Leibniz notation is a common notation in calculus that helps to identify derivaties. In Leibniz notation, the terms dx and dy are used for derivatives of x and y. This can be used with any variable. Typically this will be expressed in a fraction form, as dy / dx. This form says that you take the derivative of x in respect to y. This notation can be used for integrals as well as derivatives, although it was first developed for use with derivatives.
Tags: anti-derivative, Calculus, change, derivative, dx, dy, function, Gottfried Wilhelm Leibniz, infinitely small, integral, Leibniz, Math, notation, with respect to
Posted in Calculus | No Comments »
Thursday, October 8th, 2009
How to Use the Second Derivative Test
Description
A detailed tutorial on how to use the second derivative test. Step by step tutorial including several examples of how to use the second derivative test for reference.
Overview
The second derivative test is more well-known than the first derivative test, and is often thought to be more accurate. The second derivative test states that if the second derivative of a function is less than zero, then there is a local maximum at x. If the second derivative of a function is greater than zero, then there is a local minimum at x. However, if the second derivative of a function is equal to zero, then the local maximum or minimum cannot be determined. Then you must use the first derivative test to figure it out. The second derivative test can also be used to figure out the concavity of a function – that is, if a curve is pointing up or down. This is normally used to help create the image of the function on a graph.
Tags: Calculus, chart, concavity, critical points, curve, derivative, equals, extrema, extremum, first derivative test, function, graph, Math, maxima, maximum, minima, minimum, negative, positive, second derivative test
Posted in Calculus | No Comments »
Thursday, October 8th, 2009
How to Use the First Derivative Test
Description
A detailed tutorial on how to use the first derivative test. Step by step tutorial including several examples of how to use the first derivative test for reference.
Overview
The first derivative test involves taking the derivative of a function that you would like to find the local maximum or minimum of. Once you have the derivative, you must determine if the function is increasing or decreasing. If the derivative is positive, the function is increasing, and when the derivative is negative, the function is decreasing. If the derivative cannot be determined as positive or negative, then the test fails.
Tags: Calculus, chart, critical points, decreasing, derivative, extrema, extremum, first derivative test, function, graph, increasing, Math, maxima, maximum, minima, minimum, negative, positive, second derivative test
Posted in Calculus | No Comments »
Tuesday, September 22nd, 2009
How to Solve the Euler-Lagrange Equation
Description
A detailed tutorial on the solving of the Euler-Lagrange Equation. Step by step tutorial including several examples of how to solve the Euler-Lagrange Equation for reference.
Overview
The Euler-Lagrange Equation, sometimes just called Lagrange’s Equation, is a differential equation which has a solution that is function for which a given functional is stationary. The Euler-Lagrange Equation is an equation satisfied by a function q of a real argument t which is a stationary point of the functional 
.
After finding q, the derivative of q, and L, which can all be expressed by seperate equations. the Euler-Lagrange Equation can be written as an ordinary differential equation expressed by 
Tags: calculus of variations, derivative, differential equations, Euler-Lagrange Equation, Fermat's theorem, function, functional ordinary differential equation, Joseph Louis Lagrange, Lagrange's Equation, Leonhard Euler, Math, maxima, minima, optimization, stationary, stationary point
Posted in Differential Equations | No Comments »
Thursday, September 17th, 2009
Explanation of the Monotonicity Theorem
Description
A detailed tutorial on the solving of the Monotonicity Theorem. Step by step tutorial including several examples of how to solve the Monotonicity Theorem for reference.
Overview
The Monotonicity Theorem is used to determine if a function is increasing or decreasing. The Monotonicity Theoream states that:
If f ‘(x) > 0 the function is increasing
If f ‘(x) < 0 the function is decreasing
This is basically a repeat of information you already know. The derivative is the same as the slope of a line, and it is obvious to anyone who has spent time studying grpahs that a positive slope increases and a negative slope descreases. Simply find your function, take a derivative, and set it to either less than or greater than 0 to figure out if your graph will be increasing or decreasing.
Tags: 0, Calculus, decreasing, derivative, function, greater than, increasing, less than, Math, monotonicity, monotonicity theorem, slope, zero
Posted in Calculus | No Comments »
Thursday, September 17th, 2009
Definition of the Mean Value Theorem
Description
A detailed tutorial on the solving of the Mean Value Theorem. Step by step tutorial including several examples of how to solve the Mean Value Theorem for reference.
Overview
You can easily figure out what the Mean Value Theorem is by looking at the word mean – a mean is an average. The Mean Value Theorem states that there is at least one point on the graph of a function where the derivative is equal to the average slope of the entire section of the graph you are looking at. The requirements are that the graph is both continuous and differentiable on the interval [a, b], where a < b. Then there exists some c in (a, b) such that:
f ‘(c) = [f(b) - f(a)] / [b - a]
The Mean Value Theorem is very similar to Rolle’s Theorem, which is a more specific theorem stating the same thing.
Tags: a, average, b, c, Calculus, continuous, derivative, differentiable, interval, Math, mean, mean value theorem, rolle's theorem, slope, theorem, value
Posted in Calculus | No Comments »
Friday, September 4th, 2009
How to Solve Derivatives with Trigonometric Functions
Description
This video shows the basic trigonometric functions and their derivatives. Content is laid out in an organized and easy to follow manner.
Overview
Trigonometric functions, also known as just trig functions, are very common – they are sine, cosine, tangent, secant, cotangent, cosecant. These are derivatives that you should have memorized, because there is no good way to solve for them.
d/dx sin(x) = cos(x)
d/dx cos(x) = -sin(x)
d/dx tan(x) = sec^2(x)
d/dx sec(x) = sec(x) * tan(x)
d/dx csc(x) = -csc(x) * cot(x)
d/dx cot(x) = -csc^2(x)
Tags: Calculus, cosecant, cosine, cotangent, derivative, derivatives, differentiation, Math, secant, sine, tangent, trig, trig functions, trigonometric, trigonometric functions, trigonometry
Posted in Calculus | No Comments »
