Question

Find the derivative of $\sqrt{2}x+2\sqrt{x}-\frac{1}{x}$ ?

• A. $\sqrt{2}+1/\sqrt{x}(1-\frac{1}{2}x)$
• B. $\sqrt{2}-1/\sqrt{x}(1+\frac{1}{2}x)$
• C. $\sqrt{2}-1/\sqrt{x}(1-\frac{1}{2}x)$
• D. $\sqrt{2}+1/\sqrt{x}(1+\frac{1}{2}x)$

Answer 1

Answer: (D)

The derivative of $\sqrt{2}x+2\sqrt{x}-\frac{1}{\sqrt{x}}$
$=\sqrt{2}+2\cdot \frac{1}{2}{x}^{\frac{1}{2}-1}+\frac{1}{2}{x}^{-\frac{1}{2}-1}$
$=\sqrt{2}+x^{\frac{-1}{2}}+\frac{1}{2}{x}^{\frac{-3}{2}}$
$=\sqrt{2}+\frac{1}{\sqrt{x}}+\frac{1}{2x\sqrt{x}}$
$=\sqrt{2}+\frac{1}{\sqrt{x}}\left(1+\frac{1}{2x}\right)$