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Milentije
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I have problem like attached.
A derivative of finite sums is a mathematical concept that represents the rate of change of a function at any given point. It is calculated by finding the slope of the tangent line at that point on the function's graph.
The derivative of finite sums is important because it allows us to analyze and understand the behavior of functions. It helps us to find maximum and minimum values, identify the direction of motion for objects, and solve optimization problems.
The derivative of finite sums can be calculated using the power rule, product rule, quotient rule, or chain rule. These rules involve finding the derivative of each term in the sum and then combining them using basic algebraic operations.
Sure, let's say we have the function f(x) = 2x^3 + 5x^2 + 3x. To find its derivative, we use the power rule to get f'(x) = 6x^2 + 10x + 3. This is the derivative of the finite sum of terms 2x^3, 5x^2, and 3x.
The derivative of finite sums is used in various real-world applications such as economics, physics, engineering, and finance. For example, it can be used to determine the maximum profit for a company, the fastest route for a car to travel, or the optimal design for a bridge.