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

**Solving problem 1:**

**Y = x ^{2}+3x + 4**

**Solution:**

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

dy/dx =2x^{1}+ 3+0=2x^{1}+ 3

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

d^{2}y/dx^{2} = 2+0=2

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

d ^{3}y/dx^{3} = 0

**Solving Problem 2**

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

**Y = x ^{2}+x + 4**

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

dy/dx= 2x^{1}+ 1+0

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

d^{2}y/dx^{2}= 2+0=2

**Solving Problem 3:**

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

**Y = Sin 2****X**

**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.

d^{2}y/dx^{2}= *-4 Sin 2X*

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

d ^{3}y/dx^{3} = -8 Cos 2X

**Solving Problem 4:**

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

**Y = 2****X ^{3}+x^{2}**

**Solution:-**

Given equation is Y = 2X^{3}+x^{2}

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

dy/dx =*6x ^{2}+2x^{1}*

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

d^{2}y/dx^{2}= *12x + 2*

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

d ^{3}y/dx^{3} = *12*