do it step by step with reasons by side

Asked by ashwinikumar59 | 8th May, 2010, 06:54: AM

Expert Answer:

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.

=x (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.

 

Answered by  | 29th May, 2010, 12:00: PM

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