If \(y = 2(2x + \sqrt{x})^{2}\), find \(\frac{\mathrm d y}{\mathrm d x}\).
FURTHER MATHEMATICS
WAEC 2010
If \(y = 2(2x + \sqrt{x})^{2}\), find \(\frac{\mathrm d y}{\mathrm d x}\).
- A. \(2\sqrt{x}(2x + \sqrt{2})\)
- B. \(4(2x + \sqrt{x})(2 + \frac{1}{2\sqrt{x}})\)
- C. \(4(2x + \sqrt{x})(2 + \sqrt{x})\)
- D. \(8(2x + \sqrt{x})(2 + \sqrt{x})\)
Correct Answer: B. \(4(2x + \sqrt{x})(2 + \frac{1}{2\sqrt{x}})\)
Explanation
\(y = 2(2x + \sqrt{x})^{2}\)
Let \(u = 2x + \sqrt{x}\)
\(y = 2u^{2}\)
\(\frac{\mathrm d y}{\mathrm d u} = 4u\)
\(\frac{\mathrm d u}{\mathrm d x} = 2 + \frac{1}{2\sqrt{x}}\)
\(\therefore \frac{\mathrm d y}{\mathrm d x} = (\frac{\mathrm d y}{\mathrm d u})(\frac{\mathrm d u}{\mathrm d x})\)
= \(4u(2 + \frac{1}{2\sqrt{x}}) \)
= \(4(2x + \sqrt{x})(2 + \frac{1}{2\sqrt{x}})\)
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 Your email address will not be published.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 *