Derivative in a sentence

Its slope is the derivative ; green marks positive derivative, red marks negative derivative and black marks zero derivative.

Continuing this process, one can define, if it exists, the n th derivative as the derivative of the (n-1) th derivative.

Derivative works The NetHack GPL requires all derivative works to be distributed under the same license, except that the creator of a derivative work is allowed to offer warranty protection on the new work.

For the function the "own" second partial derivative with respect to x is simply the partial derivative of the partial derivative (both with respect to x): Chiang, Alpha C. Fundamental Methods of Mathematical Economics, McGraw-Hill, third edition, 1984.

Because the equation is second order in the time derivative, one must specify initial values both of the wave function itself and of its first-time derivative in order to solve definite problems.

By contrast, the total derivative of V with respect to r and h are respectively : and : The difference between the total and partial derivative is the elimination of indirect dependencies between variables in partial derivatives.

Choose a vector : The directional derivative of f in the direction of v at the point x is the limit : In some cases it may be easier to compute or estimate the directional derivative after changing the length of the vector.

Derivative products The original Moxie logo featuring the "Moxie Man" on the label of a derivative product.

Differentiation main Formally, the derivative of the function f at a is the limit : If the derivative exists everywhere, the function is differentiable.

Difficulty in calculating derivative of a function Newton's method requires that the derivative be calculated directly.

Discontinuous derivative If the derivative is not continuous at the root, then convergence may fail to occur in any neighborhood of the root.

Effectively, this would define the kilogram as a derivative of the ampere rather than present relationship, which defines the ampere as a derivative of the kilogram.

Geometrically, the derivative at a point is the slope of the tangent line to the graph of the function at that point, provided that the derivative exists and is defined at that point.

If a cubic polynomial has a triple root, it is a root of its derivative and of its second derivative, which is linear.

If one uses the Henstock–Kurzweil integral one can have the mean value theorem in integral form without the additional assumption that derivative should be continuous as every derivative is Henstock–Kurzweil integrable.

If the function is continuously differentiable and its derivative is not 0 at α and it has a second derivative at α then the convergence is quadratic or faster.

If the third derivative exists and is bounded in a neighborhood of α, then: : where If the derivative is 0 at α, then the convergence is usually only linear.

If x is in degrees, then : This means that the second derivative of a sine in degrees does not satisfy the differential equation : but rather : The cosine's second derivative behaves similarly.

In a way, architecture documents are third derivative from the code ( design document being second derivative, and code documents being first).

In the case of the formal derivative, there are now separate partial derivative operators, which differentiate with respect to each of the indeterminates.