Question

if y=x/x+1 then dy/dx is equal to​

Answer 1

Answer:

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Answer 2

The value of dy/dx =1/(x+1)²

Given:

y = x / x+1

To find:

The value of dy/dx

Solution:

Given  y = x / x+1  

As we know  $\frac{d}{dx} \frac{u}{v} = \frac{v \frac{du}{dx} - u \frac{dv}{dx} }{v^{2} }$  

Take u = x

⇒ $\frac{d u}{dx} = \frac{d}{dx} (x)$ = 1  

Take v = x+1

⇒ $\frac{d v}{dx} = \frac{d}{dx} (x+1)$ = $\frac{d}{dx} (x) + \frac{d}{dx} (1)$ = 1+0 = 1

⇒ $\frac{d}{dx} (x+1) = 1$  

Now substitute above values in given formula

⇒ $\frac{(x+1) (1) - x (1) }{(x+1)^{2} }$  =  $\frac{x+1 - x }{(x+1)^{2} }$  = $\frac{1 }{(x+1)^{2} }$  

The value of dy/dx =1/(x+1)²

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