Introduction to Solving online Derivatives :                        

The mathematics of the variation of a function with respect to changes in independent variables is determined by derivatives.  The most important use of derivatives is to calculate rates of change of a function and the maximum and minimum values of a function.

Example:

y = f(x).

Where f(x) is the equation of a straight line, y = m x + c,

Where m is the slope and c is the y intercept.

M = (Change in y) / (Change in X).

Through this online article you can get clear idea about how to solving derivatives.Let us see some sample problems in online.

 

Solving Online derivatives:

Solving  the following equation by differentiating  and find the first derivative second derivative and third derivative.

Solving problem 1:

Y = x2+3x + 4

Solution:

 Differentiate the above equation with respect to x to find the first derivative

dy/dx =2x1+ 3+0=2x1+ 3

To find the second derivative differentiate the first derivative of the given equation.

d2y/dx2 = 2+0=2

To find the third derivative differentiate the second derivative of the given equation.

d 3y/dx3 = 0

Solving Problem 2

  Differentiate the following equation and find the first derivative and second derivative

Y = x2+x + 4

Sol: Differentiate the above equation with respect to x to find the first derivative

dy/dx= 2x1+ 1+0

To find the second derivative differentiate the first derivative of the given equation.

d2y/dx2=  2+0=2

 

Solving Online derivatives:

Solving Problem 3:

Differentiate the following equation and find the first derivative, second derivative and third derivative

Y = Sin 2X

Solution:-

Given Y = Sin 2X.

Differentiate the above equation with respect to x to find the first derivative

dy/dx =2Cos 2X

To find the second derivative differentiate the first derivative of the given equation.

d2y/dx2= -4 Sin 2X

To find the third derivative differentiate the second derivative of the given equation.

d 3y/dx3 = -8 Cos 2X

 

 

Solving Problem 4:

Differentiate the following equation and find the first derivative, second derivative and third derivative

Y = 2X3+x2

Solution:-

Given equation is Y = 2X3+x2

Differentiate the above equation with respect to x to find the first derivative

dy/dx =6x2+2x1

To find the second derivative differentiate the first derivative of the given equation.

d2y/dx2= 12x + 2

To find the third derivative differentiate the second derivative of the given equation.

d 3y/dx3 = 12