Differentiable

Definition of Differentiable Differentiable means:  the function has derivative the derivative f’(x) must exist for every value in the function’s domain Examples The use of differentiable function When a function is differentiable, we can use all the power of calculus when working with it. When a function is differentiable, it is continuous. Differentiable ⇒ Continuous

Integration by Substitution (Reverse Chain Rule)

Definition Integration by Substitution (also called “The Reverse Chain Rule” or “u-Substitution” ) is a method to find an integral, but only when it can be set up in a special way. It is an important method in mathematics. Integration by substitution is the counterpart to the chain rule for differentiation. When it is possible to perform

Integration

Definition Integration is used to find areas, volumes, central points and often is used to find the area underneath the graph of a function. Common Functions of Integration   Function Integral Constant ∫ a dx ax + c Variable ∫ x dx Square ∫ x2 dx   Reciprocal ∫ (1/x) dx ln|x| + c Exponential ∫

Common Derivatives

Derivative of a function of a real variable measures the sensitivity to change of the function value (output) with respect to a change in its argument (input). Derivatives are a fundamental tool of calculus. The derivative of a function of a single variable at a chosen input value (when it exists) is the slope of the tangent

L’hopital’s rule: Definition, Proof, Examples

What is l’hopital’s rule L’hospital rule is one of ways to make limit easier to solve. It was introduced by French mathematicians, Guillaume de l’Hôpital. It was 1969 in his book “Analyse des Infiniment Petits pour l’Intelligence des Lignes Courbes.” L’hospital rule use derivative concept. In calculus, L’hospital use derivative to determine limit value in

Homogeneous Differential Equations

A Differential Equation is an equation with a function and one or more of its derivatives: Example: an equation with the function y and its derivative Homogeneous Differential Equations A first order Differential Equation is Homogeneous when it can be in this form: We can solve it using Separation of Variables but first we create

Implicit Differentiation

Some equations in x and y in mathematics do not explicitly define y as a function x and cannot be easily manipulated to solve for y in terms of x, even though such a function may exist. If it happen, it is implied that there exists a function y = f( x) such that the given

Integration by Parts: Formula & Examples

Integration by Parts Formula Integration is one of calculus part. Integration is not only consisting of general formula, but also integration by substitution and integration by parts. Different problem needs different way to solve it. Integration by parts was discovered by mathematicians, Brook Taylor, in 1715. Integration by parts is used to solve integration problems

Partial Derivatives: Definition, How to Find, Chain Rule, Examples

Derivative is one of mathematics operation especially in calculus. In real life it uses to determine the slope, maximum or minimum of something (income, profit, etc.). What is Partial Derivative? Partial derivative is one of way to solve derivative specific problem. In detail, the problem is more than one variable function. In other words, if

Continuous Function: Definition & Examples

Definition of Continuous Function  Function describe as a relation of each value from the first set that is associated exactly one value from another set. Function has many types in mathematics. One of them is continuous function. Continuous function is one of topics in calculus. Continue means unbroken. Continuous function is a function that has