The correct option is A 1/2√( ( x ))·cos√(x). Let y = sin√(x) Thus using chain rule #160; dydx=cos√(x). (12√(x) )=12√(x)cos√(x) ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Chain Rule of Differentiation

d/dxsin√x

Question

$\frac{d}{d x} (sin \sqrt{x})$

\frac{1}{2 \sqrt{(x)}} \cdot cos \sqrt{x} .

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{- 1}{2 \sqrt{(x)}} \cdot cos \sqrt{x} .

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1}{2 \sqrt{(x)}} \cdot sin \sqrt{x} .

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{- 1}{2 \sqrt{(x)}} \cdot sin \sqrt{x} .

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{1}{2 \sqrt{(x)}} \cdot cos \sqrt{x} .$
Let $y = sin \sqrt{x}$

Thus using chain rule

$\frac{d y}{d x} = cos \sqrt{x} . (\frac{1}{2 \sqrt{x}}) = \frac{1}{2 \sqrt{x}} cos \sqrt{x}$

Suggest Corrections

Similar questions

f (x) = x sin (\sqrt{x})

\int_{0}^{\frac{π}{2}} e^{sin x} \cdot cos x dx

\frac{d}{d x} {sin}^{- 1} (2 x \sqrt{1 - x^{2}}) = . . . . . . . | x | > \frac{1}{\sqrt{2}}

- 1 \leq x \leq 1

\frac{d}{d x} ({sin}^{- 1} (\frac{3 x}{2} - \frac{x^{3}}{2}))

\frac{d}{d x} ({sin}^{- 1} [x \sqrt{1 - x} + \sqrt{x} \sqrt{1 - x^{2}}])

Join BYJU'S Learning Program