Differentiation - Practice Questions & MCQ

DIFFERENTIATION

The rate of change of a quantity y with respect to another quantity x is callled the derivative or differential coefficient of y with respect to x. Geometrically, Differentiation of a function at a point represents slope of tanget to the graph of the function at that point.

Consider any function, y = f(x)

Let P(x, y) and Q(x + Δx, f(x + Δx)) be two points on the curve

Slope of chord PQ =         (Using two points lying on the straight line PQ)

Now as Δx ➝ 0, the point Q moves infinitesimally close to point P, and chord PQ becomes tangent to the curve at point P.

So slope of chord PQ becomes slope of the tangent to the curve at point P

So slope of tangent at P =  

This gives the slope of tangent at P. This value is also known as the derivative or differentiation of function f(x) with respect to x. 

It is also denoted by 

If we replace Δx with h, then we can write

This method to find the derivative of f(x) is also known as "First Principle of derivative" or "a-b initio method"