derivative f(y)=5x+(135)/x (15x+30)

解答

导数

f (y) = 5 x + \frac{135}{x} (15 x + 30)

5 - \frac{4050}{x ^{2}}

求解步骤

\frac{d}{d x} (5 x + \frac{135}{x} (15 x + 30))

化简

5 x + \frac{135}{x} (15 x + 30) : 5 x + \frac{135 ( 15 x + 30 )}{x}

= \frac{d}{d x} (5 x + \frac{135 ( 15 x + 30 )}{x})

使用微分加减法定则:

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

= \frac{d}{d x} (5 x) + \frac{d}{d x} (\frac{135 ( 15 x + 30 )}{x})

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

\frac{d}{d x} (\frac{135 ( 15 x + 30 )}{x}) = - \frac{4050}{x ^{2}}

= 5 - \frac{4050}{x ^{2}}

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