Differentiate \(\frac{x}{x + 1}\) with respect to x.

  • A \(\frac{x}{x + 1}\)
  • B \(\frac{-1}{x + 1}\)
  • C \(\frac{1 - x}{(x + 1)^2}\)
  • D \(\frac{1}{(x + 1)^2}\)
waec 2020furthermathematics

The correct answer is D. \(\frac{1}{(x + 1)^2}\)

\(\frac{d}{dx}(\frac{x }{x + 1}\)) = \(\frac{v\frac{du}{dx} - u\frac{dv}{dx}}{v^2}\) 

u = x, \(\frac{du}{dx}\) = 1, v = x + 1, \(\frac{dv}{dx}\) = 1

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

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

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

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