Vector Differentiation

The method through which an individual can find the derivatives of a particular function in calculus is known as differentiation. A derivative can be defined as the rate at which a particular function changes concerning another given quantity. Sir Isaac Newton developed the laws concerning Differentiation or differential calculus. The principles concerning derivatives as well as limits are utilised in several areas of science. Integration along with differentiation forms the core concepts within calculus. In this context, it should be mentioned that speed is often calculated as the rate at which distance changes with time. 

Vector differentiation

The term vector differentiation essentially means the differentiation of a given vector function. Specifically in calculus, the derivatives of certain real functions are calculated in a real variable. If we consider a single variable function such as y = g(z) then we can calculate y’s derivative based on z. However, if we consider functions of several variables such as y = g (z1, z2,…., zn) then the derivative of y is calculated based on any of the provided independent variables. However, while doing this other independent variables should be taken as fixed. 

Specifically, in the case of vector analysis, the derivatives of different functions are calculated based on any one of the independent variables. This is known as vector differentiation and it means that derivatives of a particular function of the following type are calculated.

R(v) = x(v) i + y(v) j + z(v) k, where R represents the position vector of a point Q(x, y, z) in space that moves as v increases. It traces a particular curve in space. This can be corresponded with the parametric representation of  a particular space curve which can be given as x = x (v), y = y (v), z = z(v). 

For finding derivatives we take the limit ΔR/Δv = [R (v + Δv) – R(v) / Δv. If the limit of this function exists then the derivative is given by dR/dv = (dx/dv)i + (dy/dv)j + (dz/dv)k, where R is being differentiated on the basis of time (v denoting time).

Differentiation Calculator

A differentiation calculator is an online process of calculating the differentiation of certain simple functions. There is a specific process through which the differentiation calculator calculates the differentiation of a particular function. After entering the function in the online website the parser firstly analyzes the entered mathematical function. Next, it transforms it into a form that can be understood better by a computer, preferably in the form of a tree. This derivative calculator or the differentiation calculator maintains the order of different operations. A significant specialty within a mathematical specialty is that the sign of multiplication can be sometimes left out. For instance, people normally write 6x in place of 6*x. The differentiation calculator has to identify these particular cases and insert the multiplication sign accordingly. Next, the parser is used within a Javascript that is particularly on the algorithm of Shunting yard. After this, through several different steps, the derivative of the entered function is finally calculated. A well known derivative calculator available online is the “derivative calculator with steps”

Partial derivative calculator

A partial Derivative calculator can be described as an online tool for the calculation of partial derivatives of different functions. Several sites offer this partial derivative calculator through which the partial derivative of a particular function can be easily calculated. One such site is the “Partial derivative calculator with steps”. The steps that one can follow to calculate the partial derivative of a particular function through an online website have been outlined in the following. 

1st Step: Enter the variable as well as the function in the field of input.

2nd Step: After entering the variable as well as the function select the submit button to obtain the derivative. 

3rd Step: After clicking on the submit button, the partial derivative of the entered function will appear in a whole new window along with the steps that were followed to obtain it.  

Conclusion

Throughout the article the core topic that was analysed is differentiation. Under this core topic, the definition of differentiation or derivative was first discussed. This was followed by the discussions on vector differentiation. Next, it was observed that there are several online platforms such as differentiation calculator and partial derivative calculator through which the differentiation, as well as the partial differentiation of a given function, can be effectively calculated.