Learning calculus online
Introduction for learning calculus online:
Online provides number of information and teaching services for the students. Calculus is a subdivision of mathematics that deals with the concepts of derivatives, integrals, limits, infinite series, differential equations and functions. It is also used for learning rate of change of velocity and the rate of change of acceleration and the slope of a curve and optimization.
Types of calculus - Learning calculus online
Calculus can be classified into two major kinds
Differential calculus
Integral calculus
Differential calculus:
Let as consider y = f(x) be a differentiable function. Then the quantities dx and dy are known as differentials. The differential dx is an independent variable that can be given any real number as the value. The differential 'dy' is also defined as terms of dx by the relation
dy = f '(x) dx (dx `~~` `Delta` x)
Integral calculus:
A function F(x) is knonw as an anti-derivative or integral calculus on an interval I of the function f(x) for every value of x if
F' (x) = f(x)
If the derivative of a function F(x) w.r. to x is f(x), then we can say that the integral calculus of f(x) is F(x).
`int` f(x) dx = F(x)
Example problems - Learning calculus online
Example problem 1 - Learning calculus online
If the function f(x) = x3, then find out f'(x).
Solution:
Given, f(x) = x3
Formula: `x^(n) = nx(n-1)`
f'(x) =`3 x ^(3-1)`
= `3x^2`
Answer: `3x^2`
Example problem 2 - Learning calculus online
Differentiate the given function y = e2x - 3.
Solution:
Given y = e2x - 3
We are going to differentiate the given function in the problem
`dy/dx = (d(e^(2x - 3)))/(dx)`
= e2x - 3 (2)
= 2e2x - 3
Answer: `2e^(2x - 4)`
Example problem 3 - Learning calculus online
Differentiate the given function f(x) = 4x4 + 3x3 + 2x2 + 1.
Solution:
Given, f(x) = 4x4 + 3x3 + 2x2 + 1
= `4 xx 4 x^(4 - 1) + 3 xx 3 x^ (3 - 1) + 2 xx 2 x^ (2-1)`
= 16x3 + 9x2 + 4x
Answer:
`dy/dx ` = 16x3 + 9x2 +4x
Example problem 4 - Learning calculus online
Solve the integral calculus `x^4` dx
`int`x4 dx = (x4+1) / (4 + 1) + c
= `x^5/5 + c`
Please express your views of this topic Find the Derivative by commenting on blog.
Example problem 5 - Learning calculus online
Solve the integral calculus `int``cotx/sinx` dx
`int``cotx/sinx` dx = `int`cosecx cotx dx + c
= -cosecx + c
Answer: -cosec x + c
Practicing problems - Learning calculus online
Praticing problem 1 - Learning calculus online
If the functiion f(x) = x4 + 2x3, then find f'(x).
Answer: f'(x) = 4x3 + 6x
Praticing problem 2 - Learning calculus online
Simplify: x-3
Answer: -`1/2x^2` + c
Online provides number of information and teaching services for the students. Calculus is a subdivision of mathematics that deals with the concepts of derivatives, integrals, limits, infinite series, differential equations and functions. It is also used for learning rate of change of velocity and the rate of change of acceleration and the slope of a curve and optimization.
Types of calculus - Learning calculus online
Calculus can be classified into two major kinds
Differential calculus
Integral calculus
Differential calculus:
Let as consider y = f(x) be a differentiable function. Then the quantities dx and dy are known as differentials. The differential dx is an independent variable that can be given any real number as the value. The differential 'dy' is also defined as terms of dx by the relation
dy = f '(x) dx (dx `~~` `Delta` x)
Integral calculus:
A function F(x) is knonw as an anti-derivative or integral calculus on an interval I of the function f(x) for every value of x if
F' (x) = f(x)
If the derivative of a function F(x) w.r. to x is f(x), then we can say that the integral calculus of f(x) is F(x).
`int` f(x) dx = F(x)
Example problems - Learning calculus online
Example problem 1 - Learning calculus online
If the function f(x) = x3, then find out f'(x).
Solution:
Given, f(x) = x3
Formula: `x^(n) = nx(n-1)`
f'(x) =`3 x ^(3-1)`
= `3x^2`
Answer: `3x^2`
Example problem 2 - Learning calculus online
Differentiate the given function y = e2x - 3.
Solution:
Given y = e2x - 3
We are going to differentiate the given function in the problem
`dy/dx = (d(e^(2x - 3)))/(dx)`
= e2x - 3 (2)
= 2e2x - 3
Answer: `2e^(2x - 4)`
Example problem 3 - Learning calculus online
Differentiate the given function f(x) = 4x4 + 3x3 + 2x2 + 1.
Solution:
Given, f(x) = 4x4 + 3x3 + 2x2 + 1
= `4 xx 4 x^(4 - 1) + 3 xx 3 x^ (3 - 1) + 2 xx 2 x^ (2-1)`
= 16x3 + 9x2 + 4x
Answer:
`dy/dx ` = 16x3 + 9x2 +4x
Example problem 4 - Learning calculus online
Solve the integral calculus `x^4` dx
`int`x4 dx = (x4+1) / (4 + 1) + c
= `x^5/5 + c`
Please express your views of this topic Find the Derivative by commenting on blog.
Example problem 5 - Learning calculus online
Solve the integral calculus `int``cotx/sinx` dx
`int``cotx/sinx` dx = `int`cosecx cotx dx + c
= -cosecx + c
Answer: -cosec x + c
Practicing problems - Learning calculus online
Praticing problem 1 - Learning calculus online
If the functiion f(x) = x4 + 2x3, then find f'(x).
Answer: f'(x) = 4x3 + 6x
Praticing problem 2 - Learning calculus online
Simplify: x-3
Answer: -`1/2x^2` + c