Differentiate \(\frac{x}{x + 1}\) with respect to x.
A. \(\frac{1}{x + 1}\) B. \(\frac{1}{(x + 1)^{2}}\) C. \(\frac{1 - x}{x + 1}\) D. \(\frac{1 - x}{(x + 1)^{2}}\)
Correct Answer: B
Explanation
\(y = \frac{x}{x + 1}\) Using quotient rule because the function is of the form \(\frac{u(x)}{v(x)}\) \(\frac{\mathrm d y}{\mathrm d x} = \frac{v\frac{\mathrm d u}{\mathrm d x} - u\frac{\mathrm d v}{\mathrm d x}}{v^{2}}\) \(\frac{\mathrm d y}{\mathrm d x} = \frac{(x + 1) . 1 - x . 1}{(x + 1)^{2}}\) = \(\frac{1}{(x + 1)^{2}}\)