derivative-7x^{2/3}-2+3x^{7/4}

解答

导数

- 7 x^{\frac{2}{3}} - 2 + 3 x^{\frac{7}{4}}

\frac{63 x ^{\frac{13}{12}} - 56}{12 x ^{\frac{1}{3}}}

求解步骤

\frac{d}{d x} (- 7 x^{\frac{2}{3}} - 2 + 3 x^{\frac{7}{4}})

使用微分加减法定则:

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

= - \frac{d}{d x} (7 x^{\frac{2}{3}}) - \frac{d}{d x} (2) + \frac{d}{d x} (3 x^{\frac{7}{4}})

\frac{d}{d x} (7 x^{\frac{2}{3}}) = \frac{14}{3 x ^{\frac{1}{3}}}

\frac{d}{d x} (2) = 0

\frac{d}{d x} (3 x^{\frac{7}{4}}) = \frac{21 x ^{\frac{3}{4}}}{4}

= - \frac{14}{3 x ^{\frac{1}{3}}} - 0 + \frac{21 x ^{\frac{3}{4}}}{4}

化简

- \frac{14}{3 x ^{\frac{1}{3}}} - 0 + \frac{21 x ^{\frac{3}{4}}}{4} : \frac{63 x ^{\frac{13}{12}} - 56}{12 x ^{\frac{1}{3}}}

= \frac{63 x ^{\frac{13}{12}} - 56}{12 x ^{\frac{1}{3}}}

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

d er i v a t i v e f (x) = 2 x^{2} - 196 ln (x)

\int \frac{1}{( 16 - t ^{2} ) ^{\frac{3}{2}}} d t

\int_{- 1}^{3} 30 - 3 y^{2} - \frac{9}{2} d y

\frac{d y}{d x} = \frac{1}{1 + x ^{2}}