The branch of mathematics which deals with continuous change is calculus. Calculus was found in the late 17th century. Isaac Newton and Gottfried Leibniz were the ones to invent calculus. Calculus deals with continuous changes in functions. Calculus shows the rate of change of functions with respect to time. Quantities are functions of time. Most of the quantities are the functions of time.
For example velocity = change in distance/change in time. It is a continuous rate of change. Calculus is a mathematical analysis which deals with the study of functions and limits. Calculus can be categorized into 2 types:
1. Differential calculus
2. Integral calculus
Differential and integral calculus both deal with the effect on function. When there is a moderate change in an independent variable, this may tend the function to zero.
What is Calculus?
Calculus is a branch of mathematics that deals with the derivative properties and integrals of quantities. It helps in finding the relation of function when there is a change in the variable. Both differentiation and integration have limits and functions. Differentiation helps to find the rate of change in quantity and integration finds quantity when the rate of change is known. To learn more interesting mathematical concepts please visit the Cuemath website.
Differential calculus is used to solve the problems as it finds the rate of change of functions with respect to the variables. Differentiation is the process of finding derivatives. Derivatives are used to get the maxima and minima values of any function. Differential calculus is concerned with the limit of the quotient. The derivative of a function is usually presented or simply f(x) which means the function is derivative of y with respect to the variable x.
The rate of change of a function varies with respect to an independent variable. This is known as a derivative. It is useful when there is a changing variable with the rate of change not constant. The sensitivity of one dependent variable with another independent variable is measured by derivative. Derivative means the rate of change of variable instantaneously with others.
Consider the man travels from point a to b in ‘t’ seconds. Man takes time to reach the point ‘c’ is t-1 seconds. The distance travelled by man in ‘ t-1’ seconds is called velocity that is the distance travelled divided by the time taken velocity = = where ‘x’ is variable which is distance and ‘t’ is the time taken to reach a particular point or distance. This shows the distance travelled by a man with respect to time. Differentiation is the process of finding the derivative. Let’s find the derivative of function y=f(x), which shows the value of y changes with respect to variable ‘x’.dx shows the infinitesimal change in x then the derivative of y to x is
Linear, exponential and logarithmic functions have derivative formulas listed below
- d/(d(x))(k) = 0 , where k is the constant
2 .d/(d(x))(x) = 1
3. d/(d(x))(〖x〖^n〗)〗^= n x^( n-1)
4. d/(d(x))(kx) = k ,where k is any constant
5. d/(d(x)) √x = 1/2 √x
6. d/(d(x))(1/x) = -1/x^2
7. d/(d(x))( log x) = 1/(x ), x>0
8. d/(d(x)) e^( x) = e^( x)
9. d/(d(x)) 〖(a〗^x) =〖 a^( x) log a 〗^