Examples of using Derivative of a function in English and their translations into Greek
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The first derivative of a function.
It is also interpreted as the exterior derivative of a function u.
Computing the derivative of a function and“finding the area” under its curve are"opposite" operations.
The dialog shown below is used to create the first derivative of a function.
Graphical interpretation of the derivative of a function is explored interactively using an applet.
Differential calculus is the study of the definition, properties,and applications of the derivative of a function.
Definition of the Derivative of a Function.
The total derivative of a function does not give another function in the same way as the one-variable case.
Questions on the computation and properties of the derivative of a function in calculus are presented.
The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value.
The derivative of a function can, in principle, be computed from the definition by considering the difference quotient, and computing its limit.
The common thread is that the derivative of a function at a point serves as a linear approximation of the function at that point.
The derivative of a function of a real variable measures the sensitivity to change of a quantity(a function value or dependent variable) which is determined by another quantity(the independent variable).
The definition of the derivative of a function in calculus is explored interactively using an applet.
By finding the derivative of a function at every point, it is possible to produce a new function, called the derivative function or just the derivative of the original function. .
For a real-valued function of a real variable, the derivative of a function at a point generally determines the best linear approximation to the function at that point.
The notion of a directional derivative of a function from multivariable calculus is extended in Riemannian geometry to the notion of a covariant derivative of a tensor.
In higher dimensions, the derivative of a function at a point is a linear transformation called the linearization.
The primary objects of study in differential calculus are the derivative of a function, related notions such as the differential, the derivative of a function at a chosen input value describes the rate of change of the function near that input value.
Differentiation of Inverse Functions(1), review of the formula used to find the first derivative of the inverse of a function.
The relation between the total derivative and the partial derivatives of a function is paralleled in the relation between the kth order jet of a function and its partial derivatives of order less than or equal to k.
The derivatives of a function f at a point x provide polynomial approximations to that function near x.
The notion of the derivative of such a function is obtained by replacing real variables with complex variables in the definition.
This is because the total derivative of a multivariable function has to record much more information than the derivative of a single-variable function.
Consequently the definition of the derivative for a function of one variable applies.
Derivative of a composite function and higher order derivatives.
Derivative of an inverse function.