Differential Calculus

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					                          Differential Calculus
Differential Calculus

In calculus, differentiation is the way to finding the derivatives of the given functions. It means
when we use the differentiation rules on some expression it will give us derivative of that
expression and these derivative expression are of some degree that means how many times
an expression is differentiated.

We can say it as if a function f (x) is differentiated two times then it is known as the second
degree derivative and higher degree of differentiation is also known as that degree of
differentiation.

It is very easy to find the derivative of the given expression by using the differentiate calculator
that is a online tool that gives the accurate answer in very time efficient manner means it is
online help that provide the differentiation of the particular expression that is given into the text
box of the online differentiate calculator.

It also provide the solver for generate the derivative of the function of any order. There are text
boxes provide into the online tool that having the expression and desired order of
differentiation entered by the user.

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A differentiate calculator provides the derivatives by calculating the differentiation internally. It
follows all the rules of differentiation for calculation of the derivative.

There are some examples of solving the differentiation as follows:

If we enter the expression as 6 a^2 + 2 a – 19 and want to find the first order derivative then it
will solve by using the differentiation rule as:

d / d a (6 a^2 + 2 a – 19) = d / d a (6 a ^2) + d / d a (2 a) – d / d a (19)

= 6 ( d / d a 2 ^ a) + 2 – 0

=6*2a+2

= 12 a + 2.

There are some rules of differentiation that are used in finding the derivative are as follows:

As if we want to differentiate any constant value with respect to any differentiation variable
gives always zero that means d c / d a = o where c is any constant value.

Example d / d x 23 = 0.

If we differentiate the multiple of constant then constant value as it is multiplied with the
derivative of the function as d / d x (c f) = c (d f / d x) = c f'. Here f' define the first order
derivative of the function f.

Product rule of the differentiation is define as the sum of the multiplication of the first function
with the derivative of other function and multiple of second function with derivative of the first
function that is define as:

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d / d x (f (x) . g(X)) = f (x) d / d x ( g (x)) + g (x) d / d x (f (x)).

We can define this rule by taking a simple example as:

If we have an expression as f(x) = 4 x ^2 + 3 x

Then according to the rules of differentiation d / d x (f (x)) = d / d x (4 x^2 + 3 x)

= d / d x ( 4 x^2) + d / d x (3 x)

= 4 d / d x ( x ^2) + 3 d x / d x

= 4 ( 2 x) + 3

= 8 x + 3.




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