Question

if y=x/x+1 find dy/dx

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Answer 1

Answer: 1 / (x+1)^2

Explanation:

y = x/x+1

dy/dx = d (x/x+1) / dx

d (a/b) / dx = b*(da/dx) - a(db/dx) / b^2

d (x/x+1) / dx = (x+1)*(dx/dx) - (x)*[d (x+1) / dx] / (x+1)^2

= (x+1)*(1) - (x)*[dx/dx + d(1)/dx] / (x+1)^2

= (x+1) - (x)*(1 + 0) / (x+1)^2

=  x+1 - x / (x+1)^2

=  1 / (x+1)^2

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