Binomial theorem tells that ( x + h ) n = ( C C ... C and hence ( x + h ) n – x n = h ( nx n – +... + h n – ) . Thus df x dx ....
h nx ... nx nx − . Alternatively, we may also prove this by induction on n and the product rule as follows. The result is true for n = , which has been proved earlier.
We have d dx . n d x x dx