subject: Derivative Solutions Group [print this page] Calculus (Latin, calculus, a small stone used for counting) is a branch in mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. (Source: Wikipedia)
Example Problems for Derivative Solutions Group
Derivative solutions group example problem 1:
Find the value of f'(2) of the given function f(x) = 1.4x3 - 3.1x^2 - 11x
Solution:
Given function is f(x) = 1.4x3 - 3.1x^2 - 11x
Differentiate the given function with respect to x, we get
f'(x) = (1.4 * 3)x^2 - (3.1 * 2)x - 11
= 4.2x^2 - 6.2x - 11
Substitute x = 2 in the resultant equation, we get
f'(2) = (4.2 * 2^2) - (6.2 * 2) - 11
= 16.8 - 12.4 - 11
= - 6.6
Answer:
The final answer is - 6.6
Derivative solutions group example problem 2:
Find the first derivative of the given equation t = 4.7y^2 - 5.9y^4 + 2.92y
Solution:
Given equation is t = 4.7y^2 - 5.9y^4 + 2.92y
Differentiate the given function with respect to y, we get
('dt / dy' ) = (4.7 * 2)y - (5.9 * 4)y^3 + 2.92
= - 23.6y^3 + 9.4y + 2.92
Answer:
The final answer is - 23.6y^3 + 9.4y + 2.92
Derivative solutions group example problem 3:
Find the first derivative of the given equation t = 17y^2 + 39y^4 - 2y
Solution:
Given equation is t = 17y^2 + 39y^4 - 2y
Differentiate the given function with respect to y, we get
('dt / dy' ) = (17 * 2)y + (39 * 4)y^3 - 2
= 156y^3 + 34y - 2
Answer:
The final answer is 156y^3 + 34y - 2
Practice Problems for Derivative Solutions Group
Derivative solutions group practice problem 1:
Differentiate the given function g(x) = 13x3 - 86x^2 + 568x. Find g'(x)
Answer:
The final answer is 39x^2 - 172x + 568
Derivative solutions group practice problem 2:
Find the derivative value of the function f(x) = 7x^4 + 2x^2 + 4x
Answer:
The final answer is 28x3 + 4x + 4
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