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Differentiation is a method to find the derivative or the rate of change of a function. Against the abstract theory behind differentiation, its practical technique may be carried out by algebraic manipulations using the basic three derivatives, knowledge of how to manipulate functions or the four rules of operation. Differentiation is a vital topic for Mathematics students Students pursuing Mathematics are given assignments on this topic. This being a difficult topic, students avail of Differentiation assignment help from BookMyEssay. We have expert Maths assignment help tutors who can provide you with the best writing guidance along with a proper explanation.

What is Differentiation?

Differentiation enables us to find the rates of change. It enables you to find the rate of change in velocity related to time (acceleration). It enables you to find the rate of change ‘x’ related to ‘y’. The graph of y and x is the slope of the curve. There are multiple simple rules that may be used to differentiate the functions easily. We can provide you case study help on Differentiation topics so that you solve the complicated problem easily.

There are many ways to write a derivative. However, they are all the same.

y = x2, dy/dx = 2x
It means if y= x2, y’s derivative with regard to x is 2x

(x2) = 2x
dx
It means the derivative of x2 related to x is 2x.

f(x) = x2

f(x) = x2, then the derivate of is 2x.


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Rules of Differentiation

The rules of differentiation are stated in our Differentiation essay homework help as follows:

  • General rules of differentiation
    ddx[xn]=nxn−1, where n∈R and n≠0.ddx[xn]=nxn−1, where n∈R and n≠0.
  • A constant’s derivative is zero
    ddx[k]=0ddx[k]=0
  • The derivate of a constant when multiplied by a function is equal to that constant multiplied by a derivative of a function
    ddx[k⋅f(x)]=kddx[f(x)]ddx[k⋅f(x)]=kddx[f(x)]
  • The derivative of sum is the sum of their derivatives
    ddx[f(x)+g(x)]=ddx[f(x)]+ddx[g(x)]ddx[f(x)+g(x)]=ddx[f(x)]+ddx[g(x)]
  • The derivative of a difference is equal to the difference of the derivatives.
    ddx[f(x)−g(x)]=ddx[f(x)]−ddx[g(x)]
  • The derivative of a difference is equal to the difference of the derivatives.
    ddx[f(x)−g(x)]=ddx[f(x)]−ddx[g(x)]

Uses of Differentiation

There are multiple uses of differentiation that are discussed in our Differentiation assignment help in Australia. Differential calculus is used in mathematics and it is a sub-topic of calculus that is related to the study of the rates where the quantities change. It is a traditional division of calculus and the other method is integral calculus.

The primary objective of studying differential calculus is a derivative of functions and related notions including the differential and the applications. A function’s derivative at a selected input value states the rate of change of a function at the input value. The method to find a derivative is called differentiation.

The derivative is the slope of a tangent line to the graph of a function, provided that there is derivative and also defined. For a real-valued function, the derivative function states the best linear approximation to a function. Integral calculus and differential calculus are connected to the basic theorem of calculus that states the differentiation is the opposite process of integration. BookMyEssay provides you professional Differentiation dissertation thesis help that can assist you secure top grades in your academics.

Differentiation has applications in all quantitative disciplines. In physics, the derivative of a moving body regarding time is the body’s velocity and the derivative regarding time is acceleration. In a chemical reaction, the reaction rate is called a derivative. Derivatives in operation research decide the most effective ways of transporting materials and designing factories.

Derivatives are often used for finding the minima and maxima of a function. The equations that involve derivatives are known as differential equations and they are fundamentals to describe natural phenomena. Derivatives along with their generalizations are found in many mathematics fields including functional analysis, complex analysis, measure theory, differential geometry, and abstract algebra.


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