Find the derivative of y - x 2-1A- x -x2-1-2B- x-x2-1C- 1-2 -x2-1D- none of these

The correct option is B y=√(x^2+1) x^2+1=u ....(1) ⇒du dx=2x ....(2) ⇒ y=√(u) Now, dy dx=dy du×du dx =1 2√(u)×du dx =1 2√(x^2+1)× 2x From (1) amp; (2) ...

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Standard XII

Physics

Chain Rule of Differentiation

Find the deri...

Question

Find the derivative of $y = \sqrt{x^{2} + 1}$

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none of these

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Solution

The correct option is B

$y = \sqrt{x^{2} + 1}$
$x^{2} + 1 = u . . . . (1)$
$\Rightarrow \frac{d u}{d x} = 2 x . . . . (2)$
$\Rightarrow y = \sqrt{u}$
Now, $\frac{d y}{d x} = \frac{d y}{d u} \times \frac{d u}{d x}$
= $\frac{1}{2 \sqrt{u}} \times \frac{d u}{d x}$
= $\frac{1}{2 \sqrt{x^{2} + 1}} \times 2 x$ From (1) & (2)
$\frac{d y}{d x} = \frac{x}{\sqrt{x^{2} + 1}}$

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Find the derivative of y=√x2+1

The correct option is B y=√x2+1 x2+1=u ....(1) ⇒dudx=2x ....(2) ⇒ y=√u Now, dydx=dydu×dudx =12√u×dudx =12√x2+1×2x From (1) & (2) dydx=x√x2+1

Find the derivative of $y = \sqrt{x^{2} + 1}$