CBSE Class 11-science Answered

Dear Student

y=(ax + b)ⁿ

(y+y)-y=[a(x+x)+b]ⁿ - (ax + b)ⁿ 

[(y+y)-y]/(x)=([a(x+x)+b]ⁿ - (ax+b)ⁿ)/(x)

Applying limits on both sides with x approaching to zero, will give the value of dy/dx for

_x0 y/ x = dy/dx.

_x0y/x=_x0 (ax+b)ⁿ ([(1+a.x/(ax+b))ⁿ - 1])/x

Expanding using Binomial, and ignoring higher order terms of x, for x is approaching to zero, and hence is very small.

=_x0  (ax+b)ⁿ [1 + n(a.x/(ax+b))-1]/x

=_x0 (ax+b)ⁿ n(a.x/(ax+b))/x

dy/dx = n.a.(ax+b)^n-1

Regards Topperlearning.