A derivative is a contract between two or more parties whose value is based on an agreed-upon underlying financial asset like a security or set of assets like an index. For functions that act on the real numbers it is the slope of the tangent line at a point on a graph. Derivative of a vector function with nonfixed bases.
The above formulas for the derivative of a vector function rely on the assumption that the basis vectors e 1e 2e 3 are constant that is fixed in the reference frame in which the derivative of a is being taken and therefore the e 1e 2e 3 each has a derivative of identically zero.
In mathematics the derivative of a function of a real variable measures the sensitivity to change of the function value output value with respect to a change in its argument input value. Xy is the inverse of the function yx large fracdydxfrac1fracdxdy Derivative of Trigonometric Functions and their Inverses large fracddxsin ucos ufracdudx large fracddxcos u-sin ufracdudx large fracddxtan usec2ufracdudx. That is the amount by which a function is changing at one given point. Derivative of the function y fx can be denoted as fx or yx.