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

解答

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

5 (2 x + 1)

求解步骤

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

化简

\frac{5 x ^{3} + 5 x ^{2}}{x} : 5 x (x + 1)

= \frac{d}{d x} (5 x (x + 1))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (x (x + 1))

使用微分乘法定则:

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

f = x, g = x + 1

= 5 (\frac{d x}{d x} (x + 1) + \frac{d}{d x} (x + 1) x)

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

\frac{d}{d x} (x + 1) = 1

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

化简

5 (1 \cdot (x + 1) + 1 \cdot x) : 5 (2 x + 1)

= 5 (2 x + 1)

\frac{\partial}{\partial x} (x^{3} - 3 x + 3 x y^{2})

d er i v a t i v e x^{2} 25 - x^{2}

l a pl a ce t r an s f or m sin (2 t + \frac{π}{4})

y^{^{''}} + 8 y^{^{'}} + 32 y = 0, y (0) = 0, y^{^{'}} (0) = 0

\int \frac{- x}{1 - x ^{2}} d x