Question

find dy/dx if sin(x+y)=log(x+y)

Answer 1

Hope it will be helpful for you

Answer 2

Answer:

The value of $\frac{dy}{dx}$ is -1.

Step-by-step explanation:

Given equation,

$\sin(x+y)=\log(x+y)$

Differentiating both sides with respect to x,

$\cos(x+y)(1+\frac{dy}{dx})=\frac{1}{x+y}(1+\frac{dy}{dx})$

$\cos(x+y)+\cos(x+y)\frac{dy}{dx}=\frac{1}{x+y}+\frac{1}{x+y}\frac{dy}{dx}$

$\cos(x+y)\frac{dy}{dx}-\frac{1}{x+y}\frac{dy}{dx}=\frac{1}{x+y}-\cos(x+y)$

$(\cos(x+y)-\frac{1}{x+y})\frac{dy}{dx}=\frac{1}{x+y}-\cos(x+y)$

$-(\frac{1}{x+y}-\cos(x+y))\frac{dy}{dx}=\frac{1}{x+y}-\cos(x+y)$

$\implies \frac{dy}{dx}=-1$