"Find the derivative of f(x). f(x) = sqrt (x+3) f′(x) = ______"

Identify Function: Identify the function to differentiate. f(x) = sqrt(x+3) Rewrite sqrt(x+3) as (x+3)^(1/2) for easier differentiation.Apply Chain Rule: Apply the chain rule for differentiation: d/dx[u(v(x))] = u'(v(x)) * v'(x). Let u(x) = x^(1/2) and v(x) = x + 3. Then, u'(x) = (1/2)x^(-1/2) and v'(x) = 1.Substitute and Simplify: Substitute back to find f'(x). f'(x) = (1/2)(x+3)^(-1/2) * 1 Simplify to get f'(x) = 1/(2sqrt(x+3)).

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Find the derivative of $f(x)$ . $f(x) = \sqrt{x+3}$ $\newline$ $f'(x) =$ ______

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Q. Find the derivative of

f(x)

f(x) = \sqrt{x+3}

\newline

f'(x) =

______

Identify Function: Identify the function to differentiate. $\newline$ $f(x) = \sqrt{x+3}$ $\newline$ Rewrite $\sqrt{x+3}$ as $(x+3)^{\frac{1}{2}}$ for easier differentiation.
Apply Chain Rule: Apply the chain rule for differentiation: $\frac{d}{dx}[u(v(x))] = u'(v(x)) \cdot v'(x)$ . Let $u(x) = x^{\frac{1}{2}}$ and $v(x) = x + 3$ . Then, $u'(x) = \frac{1}{2}x^{-\frac{1}{2}}$ and $v'(x) = 1$ .
Substitute and Simplify: Substitute back to find $f'(x)$ . $f'(x) = \frac{1}{2}(x+3)^{-\frac{1}{2}} \times 1$ Simplify to get $f'(x) = \frac{1}{2\sqrt{x+3}}$ .