Differentiate \(\frac{x}{x + 1}\) with respect to x.
FURTHER MATHEMATICS
WAEC 2012
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. \(\frac{1}{(x + 1)^{2}}\)
Explanation
\(y = \frac{x}{x + 1}\)
Using quotient rule because the function is of the form \(\frac{u(x)}{v(x)}\)
\(\frac{\mathrm d y}{\mathrm d x} = \frac{v\frac{\mathrm d u}{\mathrm d x} - u\frac{\mathrm d v}{\mathrm d x}}{v^{2}}\)
\(\frac{\mathrm d y}{\mathrm d x} = \frac{(x + 1) . 1 - x . 1}{(x + 1)^{2}}\)
= \(\frac{1}{(x + 1)^{2}}\)
Post an Explanation Or Report an Error
If you see any wrong question or answer, please leave a comment below and we'll take a look. If you doubt why the selected answer is correct or need additional more details? Please drop a comment or Contact us directly. Your email address will not be published. Required fields are marked *