derivative of (5x^3+7x^2/x)

解答

\frac{d}{d x} (\frac{5 x ^{3} + 7 x ^{2}}{x})

10 x + 7

求解步骤

\frac{d}{d x} (\frac{5 x ^{3} + 7 x ^{2}}{x})

化简

\frac{5 x ^{3} + 7 x ^{2}}{x} : x (5 x + 7)

= \frac{d}{d x} (x (5 x + 7))

使用微分乘法定则:

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

f = x, g = 5 x + 7

= \frac{d x}{d x} (5 x + 7) + \frac{d}{d x} (5 x + 7) x

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

\frac{d}{d x} (5 x + 7) = 5

= 1 \cdot (5 x + 7) + 5 x

化简

= 10 x + 7

\frac{d}{d x} (x - \frac{1}{9} x)

x \to 0 lim (e)

n = 1 \sum \infty \frac{n - 1}{3 n - 1}

y^{^{''}} + 1500 y = 320

d er i v a t i v e f (x) = ln (18)