Derivative Calculator Step by Step

In calculus, the rate of change of curve is called derivative. Derivative Calculator is used to find the differentiation of given function. By Using the derivative calculator we can able to find the derivative value easily. Through manual calculator we can able to solve the derivative but it quite difficult to perform the calculation. But through calculator there is no other difficulty rather than entering the question, the answer will produced automatically. we have to enter the question in function place. then enter the value in which we derivative with respect to. then the order of the respected derivative, now click the derivative button. sample derivative calculator is given.

Derivative Calculus Formulas - Derivative Calculator Step by Step:

1. n th power derivative is `d/dx` (xn) = n x(n-1)

2. Exponential derivative `d/dx` (ex) = ex

3. Logarithmic derivative `d/dx` (log x) = `1/x` .

4. Trigonometry derivative `d/dx` (sin x) = cos x

5.Trigonometry derivative `d/dx` (cos x) = - sin x

6.Trigonometry derivative `d/dx` (tan x) = sec2x

7.Trigonometry derivative `d/dx` (sec x) = sec x tan x

8.Exponential derivative `d/dx` (eax) = aeax

9.Product derivative `d/dx` (uv) = u` (dv)/(dx)` + v `(du)/(dx)` .

10.Division derivative `d/dx(u/v)` = ` [v (du)/(dx) - u (dv)/(dx)]/v^2` .

Example Problems - Derivative Calculator Step by Step:

Derivative calculator step by step problem 1:

Find the derivative of given function      x6 + 3x4 + 5x2 + 3x.

Solution:

Given function is    x6 + 3x4 + 5x2 + 3x.

Step 1:      The derivative of given function can be expressed as  `d/dx` (x6 + 3x4 + 5x2 + 3x).

Step 2:      Separate the derivative function is   `d/dx` (x6) + `d/dx`(3x4) + `d/dx` (5x2 ) + `d/dx`(3x).

Step 3:      Now we know the n th power derivative rule. That is `d/dx` (xn) = n x(n-1)

Step 4:       In the first term n = 6, So derivative of   `d/dx` (x6) = 6 x(6-1)  = 6x5

Step 5:    Differentiate all the term, we get    =   `d/dx` (x6) + `d/dx`(3x4) + `d/dx` (5x2 ) + `d/dx`(3x).

=  6 x(6-1)  +  (3)(4) x(4-1)  + (5)(2) x(2-1)  + (3)(1) x(1-1)

=  6x5 + 12x3 + 10 x + 3

Answer:  6x5 + 12x3 + 10 x + 3.


Derivative calculator step by step problem 2:

Find the derivative of given function       5x2 -  3tanx .

Solution:

Given function is   5x2 -  3tanx .

Step 1:      The derivative of given function can be expressed as  `d/dx` (5x2 -  3tanx ).

Step 2:      Separate the derivative function is    `d/dx` (5x2 ) - `d/dx`(3 tan x).

Step 3:      Now we know the n th power derivative rule. That is `d/dx` (xn) = n x(n-1)

Step 4:       In the first term n = 2, So derivative of   `d/dx` (x2) = 2 x(2-1)  = 2x

Step 5:    Differentiate all the term, we get    =   `d/dx` (x2) - `d/dx`(3 tan x).

=  2x  - 3 sec2x .

=  2x  - 3 sec2x .

Answer:   2x  - 3 sec2x .