If `(tan^(-1)x)^(y)+y^(cotx)=1,` then find `(dy)/(dx).`

Explanation

To solve the equation \((\tan^{-1} x)^{y} + y^{\cot x} = 1\) and find \(\frac{dy}{dx}\), we will use implicit differentiation. Here are the steps:

### Step 1: Differentiate both sides
We start by differentiating the equation with respect to \(x\):
\[ \frac{d}{dx} \left( (\tan^{-1} x)^{y} + y^{\cot x} \right) = \frac{d}{dx}(1) \]
This simplifies to:
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