Tangents and normals

In calculus, the quotient rule is a method for determining the derivative of any function given in the form of a quotient derived by dividing two differentiable functions. The quotient rule states that the derivative of a quotient is equal to the ratio of the result achieved by to the square of the denominator’s derivative […]

One way to obtain an expression’s derivative or differentiation in calculus is to take the ratio or division of two differentiable functions and divide it by the expression. By this, I mean that while trying to get the derivative of f(x)/g(x), we can use the rule of quotients, because both of these functions are differentiable

The calculus generally has multiple variables, but it is very similar to the single-variable calculus and is only applied to multiple variables one at a time. We get a partial derivative when we hold all but one of the independent variables of a function constant and differentiate concerning that one variable. The use of partial

The partial derivative of a function of several variables is the derivative of one of the variables. The partial derivative, in other words, illustrates how a multivariable function evolves as one of the variables changes. According to the ideal gas equation, PV=kT, a gas’s pressure is determined by both its temperature and its volume. Where

Mean Value Theorems Specifically, for every curve f(x) passing through two specified points (a, f(a)) and (b, f(b)), the mean value theorem asserts that there is at least one point on the curve (c, f(c)) at which the tangent travelling through those two points is parallel to the secant travelling through those two locations. The

In both differential and integral calculus, the mean value theorem is one of the most helpful techniques. It has significant implications in differential calculus and aids in understanding the same behavior of several functions. The mean value theorem’s hypothesis and conclusion are similar to those of the Intermediate value theorem. Lagrange’s Mean Value Theorem is

The Mean Value Theorem is a fundamental concept in calculus. The oldest variation of the mean value theorem was established in the 14th century by Parmeshwara, a mathematician from Kerala, India. Furthermore, in the 17th century, Rolle provided a simplified version of this: Rolle’s Theorem, which was only established for polynomials and was not part

The root locus of a feedback system is a graphical representation in the complex s-plane of the possible positions of its closed-loop poles for various values of a certain system parameter.  This depiction shows the probable locations of the poles for the feedback system.  This representation shows the possible locations of the poles for the

The implicit function theorem is a mechanism in mathematics that allows relations to be transformed into functions of various real variables, particularly in multivariable calculus. It is possible to do so by representing the relationship as a function graph. An individual function graph may not represent the entire relation, but such a function on a

Mathematical calculus relies heavily on Lagrange’s mean value theorem. Parmeshwara, an Indian mathematician from Kerala, initially proposed the mean value theorem in its original form in the 14th century. Rolle’s Theorem, a simpler version of this, was proposed by Rolle’s in the 17th century and proved solely for polynomials. Also, in the year 1823, Augustin