Question

Select the correct answer from the given alternative:

If y = ${\displaystyle \frac{x-4}{\sqrt{x}+2}}$, then ${\displaystyle \frac{\text{d}y}{\text{d}x}}$

विकल्प

• ${\displaystyle \frac{1}{x+4}}$

• ${\displaystyle \frac{\sqrt{x}}{{\left(\sqrt{x+ 2}\right)}^2}}$

• ${\displaystyle \frac{1}{2\sqrt{x}}}$

• ${\displaystyle \frac{x}{{(\sqrt{x}+ 2)}^2}}$

Answer 1

${\displaystyle \frac{1}{2\sqrt{x}}}$

Explanation:

y = ${\displaystyle \frac{x-4}{\sqrt{x}+2}}$

= ${\displaystyle \frac{{\left(\sqrt{x}\right)}^2-{\left(2\right)}^2}{\sqrt{x}+2}}$

= ${\displaystyle \frac{(\sqrt{x}+2)(\sqrt{x}-2)}{(\sqrt{x}+2)}}$

∴ y = ${\displaystyle \sqrt{x}-2}$

Differentiating w.r.t.x, we get

${\displaystyle \frac{\text{d}y}{\text{d}x}=\frac{1}{2\sqrt{x}}}$