The gradient of the scalar field is vector size. Thus, for its location it is required to define all components of the corresponding vector, proceeding from knowledge of distribution of the scalar field.
Instruction
1. Read in the textbook on the higher mathematics that represents a gradient of the scalar field. It is known that this vector size has the direction which is characterized by the maximum speed of recession of scalar function. Such meaning of this vector size is proved by expression for definition its component.
2. Remember that any vector is defined by sizes its component. Components of a vector are actually projections of this vector to any given coordinate axis. Thus, if the three-dimensional space is considered, then at a vector has to be three components.
3. Write down as components of the vector which is a gradient of some field are defined. Each of coordinates of such vector is equal to a derivative of scalar potential on a variable which coordinate pays off. That is, if the field gradient vector component needs to calculate "iksovy", then it is necessary to differentiate scalar function on the X variable. Pay attention that the derivative has to be private. It means that at differentiation other variables which are not participating in it need to be considered constants.
4. Write expression for the scalar field. It is known that this term means itself only scalar function of several variables which are also scalar sizes. The quantity of variables of scalar function is limited to dimension of space.
5. Differentiate separately scalar function on each variable. As a result at you three new functions will turn out. Enter each function in expression for a vector of a gradient of the scalar field. Each of the received functions actually is coefficient at a single vector of this coordinate. Thus, the final vector of a gradient has to look as a polynomial with coefficients in the form of function derivatives.