Question

find the derivative of the function \\(y = \sqrt{-3 + 7x}\\).

\\\frac{dy}{dx} = \boxed{\quad}\\

Explanation:

Rewrite the function using rational exponents

$$ y = (-3 + 7x)^{1/2} $$

Apply the chain rule and power rule

$$ \frac{dy}{dx} = \frac{1}{2}(-3 + 7x)^{-1/2} \cdot \frac{d}{dx}(-3 + 7x) $$

$$ \frac{dy}{dx} = \frac{1}{2}(-3 + 7x)^{-1/2} \cdot 7 $$

Simplify the derivative expression

$$ \frac{dy}{dx} = \frac{7}{2\sqrt{-3 + 7x}} $$

Answer:

Find the derivative of the function \(y = \sqrt{-3 + 7x}\).

\(\frac{dy}{dx} =\) <blank>\(\frac{7}{2\sqrt{-3 + 7x}}\)</blank>