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.
Having problem with Types of Differentiation keep reading my upcoming posts, i will try to help you.
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
Having problem with Types of Differentiation keep reading my upcoming posts, i will try to help you.
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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