Question

Solve using derivative: if y=1+x+x²/1-x+x²; find dy/dx​

Answer 1

Step-by-step explanation:

Here, u(x)=x2+1,v(x)=x+1u(x)=x2+1,v(x)=x+1

using quotient rule,we get

dydx=(x+1)d(x2+1)dx−(x2+1)d(x+1)dx(x+1)2dydx=(x+1)d(x2+1)dx-(x2+1)d(x+1)dx(x+1)2

=(x+1)2x−(x2+1)1(x+1)2=(x+1)2x-(x2+1)1(x+1)2

=2x2+2x−x2−1(x+1)2=x2+2x−1(x+1)2