derivative f(x)= x/(32)(sqrt(x)+\sqrt[3]{x})

解答

导数

f (x) = \frac{x}{32} (x + 3 x)

\frac{9 x + 2 x ^{\frac{1}{3}} + 6 3 x}{192}

求解步骤

\frac{d}{d x} (\frac{x}{32} (x + 3 x))

将常数提出:

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

= \frac{1}{32} \frac{d}{d x} (x (x + 3 x))

使用微分乘法定则:

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

f = x, g = x + 3 x

= \frac{1}{32} (\frac{d x}{d x} (x + 3 x) + \frac{d}{d x} (x + 3 x) x)

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

\frac{d}{d x} (x + 3 x) = \frac{1}{2 x} + \frac{1}{3 x ^{\frac{2}{3}}}

= \frac{1}{32} (1 \cdot (x + 3 x) + (\frac{1}{2 x} + \frac{1}{3 x ^{\frac{2}{3}}}) x)

化简

\frac{1}{32} (1 \cdot (x + 3 x) + (\frac{1}{2 x} + \frac{1}{3 x ^{\frac{2}{3}}}) x) : \frac{9 x + 2 x ^{\frac{1}{3}} + 6 3 x}{192}

= \frac{9 x + 2 x ^{\frac{1}{3}} + 6 3 x}{192}

\frac{\partial}{\partial y} (sin (x^{2} y))

\frac{d}{d x} ((x^{3} + 6 x)^{4})

in v erse l a pl a ce \frac{2 e ^{- 2 s}}{3 s ^{2} + 12}

3 y^{^{'}} + y = 6 t, y (0) = 3

\frac{d}{d x} (6 x + 5)