Fórum de Matemática
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Se \(f(x)=\sqrt{2x^{5}}\) , Calcule.
\(f'(x)\) e \(f'(1)\)

kustelinha,
boa noite!


\(f(x) = \sqrt{2x^5}\)

\(f(x) = \left ( 2x^5 \right )^{\frac{1}{2}}\)

\(f(x) = 2^{\frac{1}{2}} \cdot x^{\frac{5}{2}}\)

\(f(x) = \sqrt{2} \cdot x^{\frac{5}{2}}\)

\(f'(x) = \sqrt{2} \cdot \frac{5}{2} \cdot x^{\left ( \frac{5}{2} - 1 \right )}\)

\(f'(x) = \frac{5\sqrt{2} \cdot x^{\frac{3}{2}}}{2}\)

\(f'(x) = \frac{5\sqrt{2} \cdot \sqrt{x^3}}{2}\)

\(f'(x) = \frac{5\sqrt{2} \cdot x \cdot \sqrt{x}}{2}\)

\(\fbox{f'(x) = \frac{5x\sqrt{2x}}{2}}\)

\(f'(1) = \frac{5 \cdot 1 \sqrt{2 \cdot 1}}{2}\)

\(\fbox{f'(1) = \frac{5\sqrt{2}}{2}}\)

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Daniel Ferreira
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