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Jan Hill
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Homework Statement
y = 2x^2pi Give an exact answer in terms of pi
Homework Equations
The Attempt at a Solution
y' = 4pix^pi
Is this as far as I can go with this?
Jan Hill said:y = 2x^2pi Give an exact answer in terms of pi
…
y' = 4pix^pi
Is this as far as I can go with this?
Jan Hill said:I put pi because the exponent becomes 2pi - pi which equals pi
The equation is y' = 4xπ.
The derivative of y = 2x^2pi represents the rate of change of the original function at any given point. It shows how much the function is changing, or its slope, at a specific point on the graph.
The derivative of y = 2x^2pi can be found using the power rule, which states that the derivative of x^n is n*x^(n-1). In this case, n = 2, so the derivative is y' = 2*2x^(2-1) = 4x.
The slope of y = 2x^2pi is constantly changing, as it is a curve. However, at any given point, the slope can be calculated using the derivative, which is 4xπ.
The derivative of y = 2x^2pi has various applications in physics, engineering, and economics. For example, it can be used to calculate the velocity and acceleration of an object, as well as the marginal cost and revenue in business.