Question

$\frac{d}{dx}\left\{\right(1+x{)}^{\frac{1}{2}}-(1-x{)}^{\frac{1}{2}}\}$

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is A

$\frac{d}{dx}\left\{\right(1+x{)}^{\frac{1}{2}}-\frac{d}{dx}(1-x{)}^{\frac{1}{2}}\}$

We know, $\{\frac{d}{dx}{x}^n=n{x}^{n-1}\}$

$\frac{1}{2}(1+x{)}^{(\frac{1}{2}-1)}\times \frac{d}{dx}(1+x\left)\frac{1}{2}\right(1-x{)}^{(\frac{1}{2}-1)}\times \frac{d}{dx}(1-x)$

$(1+x{)}^{\frac{-1}{2}}\ast 1-\frac{1}{2}(1-x{)}^{\frac{-1}{2}}\ast (-1)$

$(\frac{1}{2\sqrt{1+x}}+\frac{1}{2\sqrt{1-x}})$

option A is correct.