Differentiate \(\frac{x}{x + 1}\) with respect to x.
Take Free Practice Test On 2026 JAMB UTME, Post UTME, WAEC SSCE, GCE, NECO SSCE
Correct Answer: Option B
Explanation:
\(y = \frac{x}{x + 1}\)
Using quotient rule because the function is of the form \(\frac{u(x)}{v(x)}\)
\(\frac{\mathrm d y}{\mathrm d x} = \frac{v\frac{\mathrm d u}{\mathrm d x} - u\frac{\mathrm d v}{\mathrm d x}}{v^{2}}\)
\(\frac{\mathrm d y}{\mathrm d x} = \frac{(x + 1) . 1 - x . 1}{(x + 1)^{2}}\)
= \(\frac{1}{(x + 1)^{2}}\)
\(y = \frac{x}{x + 1}\)
Using quotient rule because the function is of the form \(\frac{u(x)}{v(x)}\)
\(\frac{\mathrm d y}{\mathrm d x} = \frac{v\frac{\mathrm d u}{\mathrm d x} - u\frac{\mathrm d v}{\mathrm d x}}{v^{2}}\)
\(\frac{\mathrm d y}{\mathrm d x} = \frac{(x + 1) . 1 - x . 1}{(x + 1)^{2}}\)
= \(\frac{1}{(x + 1)^{2}}\)