Question

siny = x cos(a+y) find dy/dx

Answer 1

Answer:

$\frac{dy}{dx}=\frac{cos(a+y)}{cosy+xsin(a+y)}$

Step-by-step explanation:

Formula used:

Product rule of differrentiation:

$\frac{d(uv)}{dx}=u.\frac{dv}{dx}+v.\frac{du}{dx}$

Given:

siny = x cos(a+y)

Differentiate with respect to x

$cosy\frac{dy}{dx}=x.(-sin(a+y))\frac{dy}{dx}+cos(a+y).1 \\\\cosy\frac{dy}{dx}=-xsin(a+y)\frac{dy}{dx}+cos(a+y)\\\\cosy\frac{dy}{dx}+xsin(a+y)\frac{dy}{dx}=cos(a+y)\\\\(cosy+xsin(a+y))\frac{dy}{dx}=cos(a+y)\\\\\frac{dy}{dx}=\frac{cos(a+y)}{cosy+xsin(a+y)}$