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The function is $\"F(x)=\\sqrt{1-2x}\"$ .

Consider $\"f(x)=\\sqrt{x}\"$ and $\"g(x)=1-2x\"$ .

The function is in the form of composite function $\"f\\$ .

Consider $\"f(x)=\\sqrt{x}\"$ .

Differentiate on each side with respect to $\"x\"$ .

$\"\\small$

Power rule of derivatives: $\"\\frac{d}{dx}x^n=nx^{n-1}\"$ .

$\"\\small$

Consider $\"g(x)=1-2x\"$ .

Differentiate on each side with respect to $\"x\"$ .

$\"\\\\\\frac{d}{dx}g(x)=\\frac{d}{dx}\\left$

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$\"F(x)=\\sqrt{1-2x}\"$ .

Chain Rule of derivatives: $\"\\frac{d}{dx}f(g(x))=$ .

Substitute $\"\\small$ and $\"\\small$ in chain rule.

$\"\\\\F\'(x)=\\frac{1}{2}\\frac{1}{\\sqrt{1-2x}}(-2)\\\\$

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$\"\\\\F\'(x)=-\\frac{1}{\\sqrt{1-2x}}\"$ .