Question

√x/√x+1 find Dervitive​

Answer 1

d/dx √x/√(x + 1)

= d/dx √[x/(x + 1)]

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

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

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

Explanation:

√a/√b = √(a/b)

√x = x^(1/2)

Chain rule:

d/dx f(g(... w(x))) = f’(g(... w(x))) * g’(... w(x)) * ... * w’(x)

Quotient rule:

d/dx f(x)/g(x) = [f’(x)g(x) - g’(x)f(x)]/[g(x)]^2