Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: R

There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

Get extra R 1,600 off
USE CODE: askschfd09

Differentiation by Abinitio

Differentiation by abinitio

        This is also known as Differentiation by definition or Differentiation by Principle.

The fundamental method to find derivatives of a function y=f(x) with respect to x is called the First principle to find derivatives of a function.

Consider a function y= f(x)

Now if x is incremented by a value Δ x then the value of y also changes (say) by Δ y.

         y + Δy = f(x+Δx)

Thus the change in value of y, is

Δy = (y + Δy) -y


The derivative of function y = f(x) at a point (x, y) is the slope of the tangent of the function at that point.

dy/dx = lim?x→0 ?y/?x = lim?x→0 (f(x+?x)-1(x))/?x

Hence the derivative of the function y=f(x) is found by the above method.


        Find the derivatives of the function y=x2 from first principle.

It is given that y=x2

If x is incremented by Δx then y changes by Δy

        y + Δy = (x+Δx)2

The changes in y that is, Δy can be calculated as

        Δy = (y+Δy)-y=(x+Δ)2=2x ?x+(?x)2

        Δy/?x = (2x?x+(?x)2)/?x 2x + ?x

        dy/dx = lim?x→0 ?y/?x = lim?x→0 (2x+?x) = 2x

To read more, Buy study materials of Methods of Differentiation comprising study notes, revision notes, video lectures, previous year solved questions etc. Also browse for more study materials on Mathematics here.

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
Get extra R 15,000 off
USE CODE: askschfd09