Monday, June 10

Broad Differentiation

In differentiation we use different formulas. Differentiation is the process of finding the derivative of the given function. The differentiation of the function is denoted as f'(x). The function can differentiated by different variables. Broad differentiation is the process of finding the derivative value one or more time of the given function. Broad differentiation includes third derivative and fourth derivative values. Now in this article we learn about broad differentiation and their example problems.

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Example problems for broad differentiation


Broad differentiation example problem 1:
        Find the third derivative value of the given function f(x) = 5x4 - 7x2 + 61x - 9
Solution:
  Given function is f(x) = 5x4 - 7x2 + 61x - 9
Differentiate the given function with respect to x, we get
                                f'(x) = 20x3 - 14x + 61
Again differentiate the given function for finding the second derivative, we get
                               f''(x) = 60x2 - 14
For finding the third derivative, again differentiate the given function
                                f'''(x) = 120x
Answer:
      The final answer is 120x
Broad differentiation example problem 2:
        Find the third derivative value of the given function f(x) = 52x4 - 17x2 + 33x
Solution:
  Given function is f(x) = 52x4 - 17x2 + 33x
Differentiate the given function with respect to x, we get
                           f'(x) = 208x3 - 34x + 33
Again differentiate the given function for finding the second derivative, we get
                          f''(x) = 624x2 - 34
For finding the third derivative, again differentiate the given function
                          f'''(x) = 1248x
Answer:
The final answer is 1248x

Broad differentiation example problem 3:
Find the fourth derivative value of the given function f(x) = 10x4 + 4x3 + 14x2 - x
Solution:
  Given function is f(x) = 10x4 + 4x3 + 14x2 - x
Differentiate the given function with respect to x, we get
                                f'(x) = 40x3 + 12x2 + 28x - 1
Again differentiate the given function for finding the second derivative, we get
                                 f''(x) = 120x2 + 24x + 28
For finding the third derivative, again differentiate the given function
                                 f'''(x) = 240x + 24
For fourth derivative, we get
                                f''''(x) = 240
Answer:
      The final answer is 240

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