Search any question & find its solution
Question:
Answered & Verified by Expert
If $f(x)=\sqrt{x}(x \geq 0)$ and $g(x)=1+x^2$, then $(f o g)^{\prime}(1)=$
Options:
Solution:
2252 Upvotes
Verified Answer
The correct answer is:
$\frac{1}{\sqrt{2}}$
$f(x)=\sqrt{x}$ and $g(x)=1+x^2$
$f \circ g=\sqrt{1+x^2} \Rightarrow(f \circ g)^{\prime}=\frac{d}{d x} \sqrt{1+x^2}=\frac{x}{\sqrt{1+x^2}}$
$\Rightarrow \quad(f \circ g)^{\prime}(1)=\frac{1}{\sqrt{2}}$.
$f \circ g=\sqrt{1+x^2} \Rightarrow(f \circ g)^{\prime}=\frac{d}{d x} \sqrt{1+x^2}=\frac{x}{\sqrt{1+x^2}}$
$\Rightarrow \quad(f \circ g)^{\prime}(1)=\frac{1}{\sqrt{2}}$.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.