Calculus • Step-by-Step

Derivative of x / (x + 1) with Steps

Step-by-step differentiation of x / (x + 1) using the Quotient Rule. Shows intermediate steps simplifying to 1 / (x + 1)²

Problem Statement

\frac{d}{dx}[\frac{x}{x + 1}]

Final Result

f'(x) = \frac{1}{\left(x+1\right)}-\frac{x}{\left(x+1\right)^{2}}

Formula Required: Quotient Rule

Low d-high minus high d-low over the square of what's below.

\frac{d}{dx}[\frac{u}{v}] = \frac{u'v - uv'}{v^2}

2 Steps

Set up the differentiation problem with respect to variable $x$.

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

Apply the Power Rule to compute the derivative.

\frac{d}{dx} \left[ \frac{x}{x+1} \right] = \frac{1}{\left(x+1\right)}-\frac{x}{\left(x+1\right)^{2}}

Interactive Calculator

Enter any equation like 2x + 8 = 20 or x² - 5x + 6 = 0 to get step-by-step solutions.

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