Question

Differentiate the following w.r.t.x.
$y = \sqrt{ \sin \: {x}^{3} }$
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Answer 1

Answer:-

$y = \sqrt{ \sin \: {x}^{3} }$

*Differentiate w.r.t.x

$\frac{dy}{dx} = \frac{d}{dx} ( \sqrt{ \sin \: {x}^{3} } )$

$\: \: \: = \frac{1}{ 2 \sqrt{ \sin \: {x}^{3} } } \times \frac{d}{dx}( \sin {x}^{3} )$

$\: \: \: = \frac{1}{2 \sqrt{ \sin \: {x}^{3} } } \times \cos {x}^{3} \times \frac{d}{dx} ( {x}^{3} )$

$\: \: = \frac{1}{2 \sqrt{ \sin \: {x}^{3} } } \times \cos {x}^{3} \times (3 {x}^{2} )$

$\frac{dy}{dx} = \frac{3 {x}^{2} \cos {x}^{3} }{2 \sqrt{ \sin {x}^{3} } }$

#This is your correct answer.

Answer 2

ANSWER :-

Answer:-

$y = \sqrt{ \sin \: {x}^{3} }$

*Differentiate w.r.t.x

$\frac{dy}{dx}$= $\frac{d}{dx} ( \sqrt{ \sin \: {x}^{3} }$

$$\begin{lgathered}\: \: \: = \frac{1}{ 2 \sqrt{ \sin \: {x}^{3} } } \times \frac{d}{dx}( \sin {x}^{3} ) \\\end{lgathered}$$

$$\begin{lgathered}\: \: \: = \frac{1}{2 \sqrt{ \sin \: {x}^{3} } } \times \cos {x}^{3} \times \frac{d}{dx} ( {x}^{3} ) \\\end{lgathered}$$

$$\begin{lgathered}\: \: = \frac{1}{2 \sqrt{ \sin \: {x}^{3} } } \times \cos {x}^{3} \times (3 {x}^{2} ) \\\end{lgathered}$$

$$\begin{lgathered}\frac{dy}{dx} = \frac{3 {x}^{2} \cos {x}^{3} }{2 \sqrt{ \sin {x}^{3} } } \\\end{lgathered}$$

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