((x+30)\sqrt[3]{2-x})^'

解答

((x + 30) 3 2 - x)^{^{'}}

3 2 - x - \frac{x + 30}{3 ( 2 - x ) ^{\frac{2}{3}}}

求解步骤

((x + 30) 3 2 - x)^{'}

使用微分乘法定则:

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

f = x + 30, g = 3 2 - x

= (x + 30)^{^{'}} 3 2 - x + (3 2 - x)^{^{'}} (x + 30)

(x + 30)^{'} = 1

(3 2 - x)^{'} = - \frac{1}{3 ( 2 - x ) ^{\frac{2}{3}}}

= 1 \cdot 3 2 - x + (- \frac{1}{3 ( 2 - x ) ^{\frac{2}{3}}}) (x + 30)

化简

1 \cdot 3 2 - x + (- \frac{1}{3 ( 2 - x ) ^{\frac{2}{3}}}) (x + 30) : 3 2 - x - \frac{x + 30}{3 ( 2 - x ) ^{\frac{2}{3}}}

= 3 2 - x - \frac{x + 30}{3 ( 2 - x ) ^{\frac{2}{3}}}

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

x \to 3 + lim (4)

\int \frac{3}{5 x ^{3}} d x

\frac{d}{d x} ((3 x^{2} - 2 x)^{2})

x^{2} \frac{d y}{d x} + y = 0