If x+siny=logx, then dy/dx is equal to:

Question

If $x + \sin y = \log x$ , then $\frac{d y}{d x}$ is equal to:

Smart Achievers · Accepted Answer

(2)

Ans. $\frac{1 - x}{x c o s y}$

Explanation:

$\sin y + x = \log x$

On differentiating with respect to $x$ , we get

$\cos y \frac{d y}{d x} + 1 = \frac{1}{x}$

$\Rightarrow$ $\cos y \frac{d y}{d x} = \frac{1}{x} - 1$

$\Rightarrow$ $\cos y \frac{d y}{d x} = \frac{1 - x}{x}$

$\Rightarrow$ $\frac{d y}{d x} = \frac{1 - x}{x \cos y}$

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