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Parametric Differentiation

If y=x2+2x+...

Question

If $y = x^{2} + 2 x + cos y$ find $\frac{d y}{d x}$

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Solution

$y = x^{2} + 2 x + cos y \frac{d y}{d x} = 2 x + 2 - sin y \frac{d y}{d x} \frac{d y}{d x} + sin y \frac{d y}{d x} = 2 x + 2 \frac{d y}{d x} (1 + sin y) = 2 x + 2 \frac{d y}{d x} = \frac{2 x + 2}{1 + sin y}$

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