Question

y= x × sinπ/6+ π/6 × sinx find dy/dx​

Answer 1

Answer:

please see the attached document

Step-by-step explanation:

11

Answer 2

Given,

$\displaystyle\longrightarrow\sf{y=x\sin\left(\dfrac{\pi}{6}\right)+\dfrac{\pi}{6}\sin x}$

Then,

$\displaystyle\longrightarrow\sf{\dfrac{dy}{dx}=\dfrac{dx}{dx}\sin\left(\dfrac{\pi}{6}\right)+\dfrac{\pi}{6}\cdot\dfrac{d}{dx}[\sin x]}$

$\displaystyle\longrightarrow\sf{\underline{\underline{\dfrac{dy}{dx}=\sin\left(\dfrac{\pi}{6}\right)+\dfrac{\pi}{6}\cos x}}}$

Taking $\displaystyle\sf{\sin\left(\dfrac{\pi}{6}\right)=\dfrac{1}{2},}$

$\displaystyle\longrightarrow\sf{\underline{\underline{\dfrac{dy}{dx}=\dfrac{\pi}{6}\cos x+\dfrac{1}{2}}}}$