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

解答

导数

\frac{5 x ^{3} + 9 x ^{2}}{x}

10 x + 9

求解步骤

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

化简

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

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

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 5 x + 9

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

\frac{d x}{d x} = 1

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

= 1 \cdot (5 x + 9) + 5 x

化简

= 10 x + 9

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