Question
Wed March 28, 2012 By: Avi Wadhwa
 

Please explain the concept of DIFFERENTIATION in calculus(in easy language)and state the derivation of the formula d/dx *(x^n)=nx^n-1

Expert Reply
Thu March 29, 2012
The derivative is the instantaneous rate of change of a function with respect to one of its variables. This is equivalent to finding the slope of the tangent line to the function at a point.
 
df/dx = limh->0[ f(x+h) - f(x) ]/h
 
f(x) = xn, where n is a real number
f(x + h) = (x + h)n
f(x) = xn

Hence, the difference quotient is given by:


Finally, applying the limit we get

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