Solve any maths problem

Step by step

1. \frac{d}{dx}\left[\frac{x}{x + 1}\right]

   Start from the derivative to compute.

2. x \frac{d}{d x} \frac{1}{x + 1} + \frac{\frac{d}{d x} x}{x + 1}

   Product rule with u = x and v = \frac{1}{x + 1}: (uv)′ = u′v + uv′.

3. - \frac{x \frac{d}{d x} \left(x + 1\right)}{\left(x + 1\right)^{2}} + \frac{\frac{d}{d x} x}{x + 1}

   Reciprocal rule: (1/v)′ = −v′/v² with v = x + 1.

4. - \frac{x \frac{d}{d x} \left(x + 1\right)}{\left(x + 1\right)^{2}} + \frac{1}{x + 1}

   d/dx of x is 1.

5. - \frac{x \left(\frac{d}{d x} 1 + \frac{d}{d x} x\right)}{\left(x + 1\right)^{2}} + \frac{1}{x + 1}

   Sum rule: differentiate term by term.

6. - \frac{x \frac{d}{d x} x}{\left(x + 1\right)^{2}} + \frac{1}{x + 1}

   The derivative of a constant is 0.

7. - \frac{x}{\left(x + 1\right)^{2}} + \frac{1}{x + 1}

   d/dx of x is 1.

8. \frac{1}{\left(x + 1\right)^{2}}

   Simplify.