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What is the derivative with respect to vector of the given function?
The derivative with respect to a vector of a function is a vector of partial derivatives of the function with respect to each component of the vector.
What is the derivative of the cross product with respect to a given variable?
The derivative of the cross product with respect to a given variable is a vector that represents how the cross product changes as that variable changes.
What is the third derivative of the function x with respect to time, denoted as d3x/dt3?
The third derivative of the function x with respect to time is the rate of change of the acceleration of x with respect to time. It is denoted as d3x/dt3.
How can one determine the velocity vector from a given position in a physical system?
To determine the velocity vector from a given position in a physical system, you can calculate the derivative of the position vector with respect to time. This derivative gives you the velocity vector, which represents the speed and direction of motion at that specific point in the system.
3 types of vector in speed velocity and accelaration?
Displacement vector: Represents the change in position of an object from its initial point to its final point. Velocity vector: Represents the rate at which an object's position changes with respect to time, including both speed and direction. Acceleration vector: Represents the rate at which an object's velocity changes with respect to time, including both magnitude and direction.
What is the derivative with respect to vector of the given function?
The derivative with respect to a vector of a function is a vector of partial derivatives of the function with respect to each component of the vector.
What is the scientific meaning of acceleration?
Definition: Acceleration is the rate of change of velocity as a function of time. It is vector. In calculus terms, acceleration is the second derivative of position with respect to time or, alternately, the first derivative of the velocity with respect to time.
What is the derivative of the cross product with respect to a given variable?
The derivative of the cross product with respect to a given variable is a vector that represents how the cross product changes as that variable changes.
What is the third derivative of the function x with respect to time, denoted as d3x/dt3?
The third derivative of the function x with respect to time is the rate of change of the acceleration of x with respect to time. It is denoted as d3x/dt3.
How can one determine the velocity vector from a given position in a physical system?
To determine the velocity vector from a given position in a physical system, you can calculate the derivative of the position vector with respect to time. This derivative gives you the velocity vector, which represents the speed and direction of motion at that specific point in the system.
3 types of vector in speed velocity and accelaration?
Displacement vector: Represents the change in position of an object from its initial point to its final point. Velocity vector: Represents the rate at which an object's position changes with respect to time, including both speed and direction. Acceleration vector: Represents the rate at which an object's velocity changes with respect to time, including both magnitude and direction.
What is the gradient of a dot product and how is it calculated?
The gradient of a dot product is a vector that represents the rate of change of the dot product with respect to each variable. It is calculated by taking the derivative of the dot product with respect to each variable and combining them into a vector.
What is the translational speed of the particle at point a?
The translational speed of a particle at a point is the magnitude of the particle's velocity vector at that point. It is given by the derivative of the position vector with respect to time evaluated at that point.
What is the difference between the differentiation of the function and the partial differentiation of the function?
You can differentiate a function when it only contains one changing variable, like f(x) = x2. It's derivative is f'(x) = 2x. If a function contains more than one variable, like f(x,y) = x2 + y2, you can't just "find the derivative" generically because that doesn't specify what variable to take the derivative with respect to. Instead, you might "take the derivative with respect to x (treating y as a constant)" and get fx(x,y) = 2x or "take the derivative with respect to y (treating x as a constant)" and get fy(x,y) = 2y. This is a partial derivative--when you take the derivative of a function with many variable with respect to one of the variables while treating the rest as constants.
What is the difference between differential and derivative in the field of calculus?
The derivative refers to the rate at which a function changes with respect to another measure. The differential refers to the actual change in a function across a parameter. The differential of a function is equal to its derivative multiplied by the differential of the independent variable . The derivative of a function is the the LIMIT of the ratio of the increment of a function to the increment of the independent variable as the latter tends to zero.
What is the derivative of 4xy3?
The derivative with respect to 'x' is 4y3 . The derivative with respect to 'y' is 12xy2 .
What is the second derivative of a function's indefinite integral?
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.
