Question

If $sin(x+y)=lo{g}_e(x+y)$, then $\frac{dy}{dx}$ is equal to

• A. 2
• B. -2
• C. 1
• D. -1

Answer 1

The correct option is D -1

$\because$ $sin(x+y)=lo{g}_e(x+y)$,
$cos(x+y)(1+\frac{dy}{dx})=\frac{1}{(x+y)}(1+\frac{dy}{dx})\Rightarrow (1+\frac{dy}{dx})\left(cos\right(x+y)-\frac{1}{x+y})=0\because cos(x+y)-\frac{1}{(x+y)}\ne 0\therefore 1+\frac{dy}{dx}=0\therefore \frac{dy}{dx}=-1$