Question

If y= x sin y.prove that dy/dx = y/[x(1- x cos y)].

Answer 1

Hence proved.
Hope it will be helpful for you

Answer 2

Answer:

$\dfrac{dy}{dx} = \dfrac{y}{x(1-xcosy)}$

Step-by-step explanation:

Here, the given equation is

$y = x siny...................(1)$

differentiate equation (1) with respect to x , we get

$\dfrac{dy}{dx} = sin y + xcosy \dfrac{dy}{dx} \\\\\dfrac{dy}{dx} -xcosy\dfrac{dy}{dx} = siny\\\\\dfrac{dy}{dx} (1-cosy)= siny................(2)$

find the value of sin y from equation (1), we get

$y = x siny\\siny=\dfrac{y}{x}$

putting the value of sin y in equation (2), we get

$\dfrac{dy}{dx}(1-xcosy)=\dfrac{y}{x} \\\\\dfrac{dy}{dx} = \dfrac{y}{x(1-xcosy)}$

hence proved