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well, the second derivative is the derivative of the first derivative. so, the 2nd derivative of a function's indefinite integral is the derivative of the derivative of the function's indefinite integral. the derivative of a function's indefinite integral is the function, so the 2nd derivative of a function's indefinite integral is the derivative of the function.

Q: What is the second derivative of a function's indefinite integral?

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The Geometrical meaning of the second derivative is the curvature of the function. If the function has zero second derivative it is straight or flat.

The first derivative is the rate of change, and the second derivative is the rate of change of the rate of change.

Yes.

No. A quadratic equation always has a second derivative that is a constant. For example -3x2 + 10x - 2 first derivative -6x + 10 second derivative -6

d/dx(X^4) = 4X^3 ( first derivative ) d/dx(4X^3) = 12X^2 ( second derivative )

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the product rule is included in calculus part.Product Rule : Use the product rule to find the derivative of the product of two functions--the first function times the derivative of the second, plus the second function times the derivative of the first. The product rule is related to the quotient rule, which gives the derivative of the quotient of two functions, and the chain rule, which gives the derivative of the composite of two functionsif you need more explanation, i want you to follow the related link that explains the concept clearly.

The Geometrical meaning of the second derivative is the curvature of the function. If the function has zero second derivative it is straight or flat.

All it means to take the second derivative is to take the derivative of a function twice. For example, say you start with the function y=x2+2x The first derivative would be 2x+2 But when you take the derivative the first derivative you get the second derivative which would be 2

The first derivative is the rate of change, and the second derivative is the rate of change of the rate of change.

2x is the first derivative of x2.

2x is the first derivative of x2.

Yes.

Afetr you take the first derivative you take it again Example y = x^2 dy/dx = 2x ( first derivative) d2y/dx2 = 2 ( second derivative)

To get the second derivative of potential energy, you first need to calculate the first derivative of potential energy with respect to the variable of interest. Then, you calculate the derivative of this expression. This second derivative gives you the rate of change of the slope of the potential energy curve, providing insight into the curvature of the potential energy surface.

the second derivative at an inflectiion point is zero

No. A quadratic equation always has a second derivative that is a constant. For example -3x2 + 10x - 2 first derivative -6x + 10 second derivative -6

d/dx(X^4) = 4X^3 ( first derivative ) d/dx(4X^3) = 12X^2 ( second derivative )