derivative of (sqrt((x^2+5^3))/9+3)

解答

\frac{d}{d x} \frac{( x ^{2} + 5 ) ^{3}}{9} + 3

\frac{x x ^{2} + 5}{3}

求解步骤

\frac{d}{d x} \frac{( x ^{2} + 5 ) ^{3}}{9} + 3

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} \frac{( x ^{2} + 5 ) ^{3}}{9} + \frac{d}{d x} (3)

\frac{d}{d x} \frac{( x ^{2} + 5 ) ^{3}}{9} = \frac{x x ^{2} + 5}{3}

\frac{d}{d x} (3) = 0

= \frac{x x ^{2} + 5}{3} + 0

化简

= \frac{x x ^{2} + 5}{3}

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