Question

differential the following w.r.t.x y=√sinx3​

Answer 1

Answer:

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

Step-by-step explanation:

$\sf \: Let's \: \: \red{ y = \sqrt{sin \: x {}^{3} } } \\ \\ \sf differentiate \: with \: respect \: x. \\ \\ \leadsto \sf\frac{d}{dx} (y) = \frac{d}{dx} ( \sqrt{sin \: x {}^{3} } ) \\ \\ \leadsto \sf \: \frac{dy}{dx} = \frac{1}{ \sqrt[2]{sin \: x {}^{3} } } \: . \: \frac{d}{dx} (sin \: x {}^{3} ) \\ \\ \leadsto \sf \: \frac{dy}{dx} = \frac{1}{ \sqrt[2]{sin \: x {}^{3} } } \: (cos \: x {}^{3} ) \: \frac{d}{dx} (x {}^{3} ) \\ \\ \leadsto \sf \: \frac{dy}{dx} = \frac{1}{ \sqrt[2]{sin \: x {}^{3} } } \: (cos \: x {}^{3} ) \: (3x {}^{2} ) \\ \\ \leadsto \sf \: \frac{dy}{dx} = \frac{3}{2} x {}^{2} \: { \frac{cos \: x {}^{3} }{ \sqrt{sin \: x {}^{3} } } } \\ \\ \leadsto \boxed{ \pink{\sf \: \frac{d}{dx} ( \sqrt{sin \: x {}^{3} } ) = \frac{3}{2} x {}^{2} \: \frac{cos \: x {}^{3} }{ \sqrt{sin \: x {}^{3} } } }} \green \bigstar$