Question

If sin y + x = log x, then dy/dx is A) 1/(x cos y) B) 1/(x sin y) C) (1- x)/(x cos y) D) (1+ x)/(x sin y)

Answer 1

Answer:

       C) (1-x)/(x cos y)

Step-by-step explanation:

$\displaystyle \sin y + x = \log x\\\\\Rightarrow (\cos y)\tfrac{dy}{dx} + 1 = \tfrac1x\quad\text{(by Chain Rule for first term)}\\\\\Rightarrow\frac{dy}{dx}=\frac{\tfrac1x-1}{\cos y}\\\\\Rightarrow\frac{dy}{dx}=\frac{1-x}{x\cos y}$