Q104 / 160 · TS EAMCET 2023 (14 May Shift 2) · Mathematics

If $f(x)=\sqrt{x}(x \geq 0)$ and $g(x)=1+x^2$, then $(f o g)^{\prime}(1)=$

  • A
    1
  • B
    $\frac{1}{2}$
  • C
    $\sqrt{2}$
  • Correct answer
    D
    $\frac{1}{\sqrt{2}}$

Solution

$f(x)=\sqrt{x}$ and $g(x)=1+x^2$ $f \circ g=\sqrt{1+x^2} \Rightarrow(f \circ g)^{\prime}=\frac{d}{d x} \sqrt{1+x^2}=\frac{x}{\sqrt{1+x^2}}$ $\Rightarrow \quad(f \circ g)^{\prime}(1)=\frac{1}{\sqrt{2}}$.

Hence, the correct answer is option: 'D'.

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