If y = x sin(a + y), prove that dy/dx = (sin^2(a + y))/(sin (a + y) - y cos(a + y))

Question

If y = x sin(a + y), prove that \(\cfrac{dy}{d\mathrm x} \) = \(\cfrac{sin^2(a+y)}{sin(a+y)-y\,cos(a+y)}\)

Answer 1

Here

y = x sin (a + y)

Differentiating it with respect to x using the chain rule and product rule,

Hence Proved.